WJEC GCSE Maths
Topic questions Statistics Probability experiments and frequency
92 questions · 424 marks · about 9.5 hours
There are 200 pupils in a school hall.
The pupils are from Year 7 to Year 11.
One of the pupils is chosen at random.
Complete the table below.
| Year 7 | Year 8 | Year 9 | Year 10 | Year 11 | |
| Probability | 0∙2 | 0∙3 | 0∙26 | 0∙14 |
How many of the pupils are in Year 10?
Darren has a bag containing red counters, yellow counters and green counters.
Altogether, there are 8 counters in the bag.
Darren chooses a counter from the bag at random.
On the probability scale below, R shows the probability that Darren chooses a red counter.
There is 1 yellow counter in the bag.
On the probability scale, mark with a Y the probability that Darren chooses a yellow
counter.
On the probability scale, mark with a G the probability that Darren chooses a green
counter.
Two groups of people, Group A and Group B, took part in Adam’s survey.
Adam asked each person this question: “From the colours Red, Blue and Green, which is your favourite colour?” There are 92 people in Group A. The results for Group A are shown in the pie chart below.
The results for Group B are shown in the pictogram below.
Adam chose one person at random from all the people in both groups.
What is the probability that this person chose Green?
A group of 100 pupils attended their school sports day.
13 pupils did not compete in either Track or Field events. The expressions in the following Venn diagram represent the number of pupils in each category. The universal set, ε, contains all the pupils.
Find the value of x.
One pupil is chosen at random from the group.
What is the probability that this pupil competed only in Track events?
In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
Two groups of people, Group A and Group B, took part in Adam’s survey. Adam asked each person this question: “From the colours Red, Blue and Green, which is your favourite colour?” There are 92 people in Group A. The results for Group A are shown in the pie chart below.
The results for Group B are shown in the pictogram below.
Adam chose one person at random from all the people in both groups.
What is the probability that this person chose Green?
A charity is organising a game using this fair spinner.
In the game, each player spins the spinner once.
100 players each pay £x to play the game once. Each player who gets an even number on the spinner wins £3.
The charity expects to make a profit of £130.
Find the value of x.
You must show all your working.
A group of 100 pupils attended their school sports day.
13 pupils did not compete in either Track or Field events. The expressions in the following Venn diagram represent the number of pupils in each category. The universal set, ε, contains all the pupils.
Find the value of x.
One pupil is chosen at random from the group.
What is the probability that this pupil competed only in Track events?
In this question you will be assessed on the quality of your organisation, communication and accuracy in writing.
A charity is organising a game using this fair spinner.
In the game, each player spins the spinner once.
100 players each pay £x to play the game once. Each player who gets an even number on the spinner wins £3.
The charity expects to make a profit of £130.
Find the value of x.
You must show all your working.
Megan has the following 7 playing cards.
She turned these cards face down. Megan then chose a card at random and recorded the number.
What is the probability that Megan recorded the number 5?
Circle your answer.
What is the probability that Megan recorded a square number?
Circle your answer.
Megan chooses a card at random 91 times. How many times would you expect Megan to record a square number?
You must show all your working.
A bag contains 1 yellow counter and 2 pink counters.
Olga puts more yellow counters into the bag.
She takes one counter out of the bag at random. The probability of taking a yellow counter out of the bag is 
How many more yellow counters did Olga put into the bag?
Olga put……………........ ……….. more yellow counters into the bag
Megan has the following 7 playing cards.
She turned these cards face down. Megan then chose a card at random and recorded the number.
What is the probability that Megan recorded the number 5?
Circle your answer.
What is the probability that Megan recorded a square number?
Circle your answer.
Megan chooses a card at random 91 times. How many times would you expect Megan to record a square number?
You must show all your working.
A bag contains 1 yellow counter and 2 pink counters.
Olga puts more yellow counters into the bag.
She takes one counter out of the bag at random. The probability of taking a yellow counter out of the bag is 
How many more yellow counters did Olga put into the bag?
Olga put……………........ ……….. more yellow counters into the bag
Also involves The four operations
PowrUp is a company that makes batteries.
The quality of the batteries is tested regularly. PowrUp calculates the relative frequency of faulty batteries after checking a total of 1000, 2000, 3000, 4000 and 5000 batteries. The results are plotted on the graph below.
One battery is selected at random. Write down the best estimate for the probability that this battery will be faulty.
You must give a reason for your choice.
Reason:
PowrUp is a company that makes batteries.
The quality of the batteries is tested regularly. PowrUp calculates the relative frequency of faulty batteries after checking a total of 1000, 2000, 3000, 4000 and 5000 batteries. The results are plotted on the graph below.
One battery is selected at random. Write down the best estimate for the probability that this battery will be faulty.
You must give a reason for your choice.
Reason:
In a game, each competitor will have 20 attempts at throwing a ball into a bucket.
They will get 1 point for every ball that lands in the bucket.
Sioned wants to keep a record of the total points for each competitor. She decides to show the results in a table with the total points recorded in groups of equal width.
She starts to draw a table using five groups, as shown below.
Explain why these groups will not be suitable.
Sioned considers using the table shown below. She decides that it is suitable for recording all the total points in groups of equal width
Fill in the two missing numbers in the top row.
Finally, Sioned decides to use the groups shown in the table below. The results for the first 100 competitors are shown in the table.
| Total points | 0 to 2 | 3 to 5 | 6 to 8 | 9 to 11 | 12 to 14 | 15 to 17 | 18 to 20 |
| Number of competitors | 5 | 10 | 17 | 22 | 23 | 12 | 11 |
One of these 100 competitors is chosen at random.
What is the probability that this competitor scored 6, 7 or 8 points?
Explain why the following statement may be incorrect.
The probability that this competitor scored 19 points is. 
Ahmed organises a game using two fair spinners, as shown below.
The first spinner shows the values 10, 20, 30 and 40. The second spinner shows the values 1, 2, 3, 4 and 5.
In the game, the two spinners are spun and the values shown are added to give a score. For example, the spinners above score 32.
Ahmed charges £1 for each attempt at the game. Any player who scores 43 or more wins £5.
Calculate Ahmed’s expected profit when this game is played 100 times.
The employees of a company belong to one of three departments: Management (M), Sales (S) or Distribution (D).
The diagram below is a sketch of a pie chart. The diagram shows the proportion of employees working in each of these departments.
An employee is chosen at random. Calculate the probability that this employee works in the Distribution department.
Give your answer as a decimal.
In a game, each competitor will have 20 attempts at throwing a ball into a bucket.
They will get 1 point for every ball that lands in the bucket.
Sioned wants to keep a record of the total points for each competitor. She decides to show the results in a table with the total points recorded in groups of equal width.
She starts to draw a table using five groups, as shown below.
Explain why these groups will not be suitable.
Sioned considers using the table shown below. She decides that it is suitable for recording all the total points in groups of equal width
Fill in the two missing numbers in the top row.
Finally, Sioned decides to use the groups shown in the table below. The results for the first 100 competitors are shown in the table.
| Total points | 0 to 2 | 3 to 5 | 6 to 8 | 9 to 11 | 12 to 14 | 15 to 17 | 18 to 20 |
| Number of competitors | 5 | 10 | 17 | 22 | 23 | 12 | 11 |
One of these 100 competitors is chosen at random.
What is the probability that this competitor scored 6, 7 or 8 points?
Explain why the following statement may be incorrect.
The probability that this competitor scored 19 points is. 
Ahmed organises a game using two fair spinners, as shown below.
The first spinner shows the values 10, 20, 30 and 40. The second spinner shows the values 1, 2, 3, 4 and 5.
In the game, the two spinners are spun and the values shown are added to give a score. For example, the spinners above score 32.
Ahmed charges £1 for each attempt at the game. Any player who scores 43 or more wins £5.
Calculate Ahmed’s expected profit when this game is played 100 times.
The employees of a company belong to one of three departments: Management (M), Sales (S) or Distribution (D).
The diagram below is a sketch of a pie chart. The diagram shows the proportion of employees working in each of these departments.
An employee is chosen at random. Calculate the probability that this employee works in the Distribution department.
Give your answer as a decimal.
At lunchtime on Wednesday, a café had 19 customers.
• 7 of these customers bought a meal and a drink. • 2 of these customers did not buy a meal or a drink. • The total number of customers who bought a meal was twice the total number of customers who bought a drink.
One of these customers is chosen at random.
What is the probability that this customer bought a meal?
At lunchtime on Wednesday, a café had 19 customers.
• 7 of these customers bought a meal and a drink. • 2 of these customers did not buy a meal or a drink. • The total number of customers who bought a meal was twice the total number of customers who bought a drink.
One of these customers is chosen at random.
What is the probability that this customer bought a meal?
Also involves Factors, multiples and primes
A pencil case contains some pens. One pen is chosen at random. The probability that the chosen pen is blue is 45%.
What is the probability that the chosen pen is not blue?
Dewi throws a fair six-sided dice. What is the probability that Dewi throws a prime number?
Circle your answer.
A pencil case contains some pens. One pen is chosen at random. The probability that the chosen pen is blue is 45%.
What is the probability that the chosen pen is not blue?
Dewi throws a fair six-sided dice. What is the probability that Dewi throws a prime number?
Circle your answer.
Two fair spinners are shown below.
In a game, the numbers shown by the two pointers are added together. In the diagram, the score gained would be 2 + 3 = 5.
A winning score is 6 or more.
How many winning scores would you expect when the game is played 60 times?
You must show all your working.
A box contains different-coloured balls. Some are red, some are blue and the others are green.
The bar chart shows how many balls of each colour are in the box.
Draw an accurate pie chart to compare the number of coloured balls in the box.
Part of the pie chart has been completed for you.
The letters A, B, C and D describe four different events.
| Experiment | Event |
| A fair 6-sided dice is thrown. | A 4 is thrown. |
| A fair coin is thrown. | B A tail is thrown. |
| Four cards labelled North, East, South and West are placed in a box. One card is chosen at random. | C North is chosen. |
| Seven cards, each labelled with a different day of the week, are placed in a box. One card is chosen at random. | D Sunday is chosen. |
Using the letters A, B, C and D, list the events in the order of how likely they are to happen.
Start with the least likely and end with the most likely.
A bus going to a Welsh Heritage conference has 43 people on board.
There are 38 students, 4 tutors and a driver on the bus.
At the conference, each student will attend a session on Language, a session on History or both sessions.
• All the students will attend at least one session. • 18 students will attend both sessions. • 25 students will attend the session on History. • The tutors and driver will not attend either of the sessions.
One of the people on the bus is chosen at random.
What is the probability that this person will attend the session on Language?
Mary has 6 oranges and 11 apples in a bag. She chooses one piece of fruit from the bag at random.
What is the probability that Mary chooses an apple?
Also involves Fractions
Samira has a dice. Its faces are numbered 1 to 6. She wants to know whether her dice is biased or not. Samira rolled this dice 300 times. Her results are shown in the table below.
| Number shown on dice | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 65 | 40 | 52 | 10 | 23 | 110 |
The relative frequency of throwing a 5 is 
What is the relative frequency of throwing a 2?
Give your answer as a fraction in its simplest form.
The 22 pupils in a class were asked, “What is your favourite pet?” The pets chosen by the pupils were dog, cat, rabbit and hamster. Some of the results are shown in the bar chart below.
9 pupils in the class chose either rabbit or hamster. The modal pet is rabbit.
Complete the bar chart by drawing the two missing bars.
Frequency
One of these pupils is chosen at random.
What is the probability that this pupil’s favourite pet is a cat?
Mark is making an 8-sided spinner. All of the sections on his spinner are identical.
Mark is going to label each of the sections with one of three colours: blue (B), yellow (Y) or red (R).
Label the spinner below so that when the spinner is spun: • landing on red and landing on blue are equally likely AND
• it is likely that the spinner lands on yellow.
Laura puts 90 counters in a bag.
Each counter is red or blue or yellow.
Laura wants to draw a pie chart to show the number of counters of each colour. The table below shows some of the information that she needs.
| Number of counters | Pie chart angle | |
| Red | 25 | ....................................................... |
| Blue | ....................................................... | 180° |
| Yellow | ....................................................... | ....................................................... |
| Total = 90 |
Complete the table.
You must show all your working.
Complete the pie chart to show the results.
Laura chooses a counter at random from the bag.
Calculate the probability that this counter is either red or blue.
125 pupils were asked which one of four primary schools they attended.
One of the pupils is chosen at random.
Complete the table below to find the probability that the pupil chosen went to
Ysgol Bryn.
| Ysgol Aber | Ysgol Bryn | Ysgol Castell | Ysgol Dewi | |
| Probability | 0∙08 | ......................... | 0∙2 | 0∙28 |
How many of the 125 pupils went to Ysgol Dewi?
Samira has a dice. Its faces are numbered 1 to 6. She wants to know whether her dice is biased or not. Samira rolled this dice 300 times. Her results are shown in the table below.
| Number shown on dice | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 65 | 40 | 52 | 10 | 23 | 110 |
The relative frequency of throwing a 5 is 
.
What is the relative frequency of throwing a 2?
Give your answer as a fraction in its simplest form.
Do the results in the table suggest that Samira’s dice is biased?
Yes No
Explain your decision.
This dice is thrown 2400 times. Use Samira’s results to calculate the number of times you would expect a 6 to be
thrown.
In a group of 200 people:
• 105 people do not have black hair and do not wear glasses • 20 people have black hair and wear glasses • 70 people have black hair.
Laura puts 90 counters in a bag.
Each counter is red or blue or yellow.
Laura wants to draw a pie chart to show the number of counters of each colour. The table below shows some of the information that she needs.
| Number of counters | Pie chart angle | |
| Red | 25 | ....................................................... |
| Blue | ....................................................... | 180° |
| Yellow | ....................................................... | ....................................................... |
| Total = 90 |
Complete the table.
You must show all your working.
Complete the pie chart to show the results.
Laura chooses a counter at random from the bag.
Calculate the probability that this counter is either red or blue.
125 pupils were asked which one of four primary schools they attended.
One of the pupils is chosen at random.
Complete the table below to find the probability that the pupil chosen went to
Ysgol Bryn.
| Ysgol Aber | Ysgol Bryn | Ysgol Castell | Ysgol Dewi | |
| Probability | 0∙08 | ......................... | 0∙2 | 0∙28 |
How many of the 125 pupils went to Ysgol Dewi?
In a group of 200 people:
• 105 people do not have black hair and do not wear glasses • 20 people have black hair and wear glasses • 70 people have black hair.
A bag contains red balls, green balls and yellow balls. The number of green balls is equal to the number of yellow balls.
Mali picks one ball from the bag at random. The probability that she will pick a red ball is 0·3.
Find the probability that Mali will pick a yellow ball.
A different bag contains 10 balls. Some of the balls in the bag are blue. All the other balls are white. Morgan picks a ball from the bag at random. He says,
Explain why Morgan cannot be correct.
Two fair spinners are shown in the diagram above. In a game, the two spinners are spun.
The two numbers obtained are multiplied together to get a score. For example, in the diagram above, the score is 6 because 3 
2 
6.
Some of the scores are shown in the table below.
Complete the table to show all the possible scores.
Explain why all the scores are even numbers.
What is the probability that a person gets a score of 10 or more when playing the game
once?
Players are charged £2.50 to play the game once. Each player who gets a score of 10 or more wins £3.50. How much profit would you expect to make when 228 people each play the game once?
You must show all your working.
A bag contains red balls, green balls and yellow balls. The number of green balls is equal to the number of yellow balls.
Mali picks one ball from the bag at random. The probability that she will pick a red ball is 0·3.
Find the probability that Mali will pick a yellow ball.
A different bag contains 10 balls. Some of the balls in the bag are blue. All the other balls are white. Morgan picks a ball from the bag at random. He says,
Explain why Morgan cannot be correct.
The children in year 5 and year 6 in a primary school took part in a survey.
The children were asked, “How many pets do you have?” The results are shown in the pie chart and bar chart below. No child in either year had more than 5 pets.
There are 36 children in year 5.
One child is chosen at random from all the children in year 5 and year 6.
What is the probability that this child has no more than 1 pet?
Two fair spinners are shown in the diagram above. In a game, the two spinners are spun.
The two numbers obtained are multiplied together to get a score. For example, in the diagram above, the score is 6 because 3 2 
6.
Some of the scores are shown in the table below.
Complete the table to show all the possible scores.
Explain why all the scores are even numbers.
What is the probability that a person gets a score of 10 or more when playing the game
once?
The children in year 5 and year 6 in a primary school took part in a survey.
The children were asked, “How many pets do you have?” The results are shown in the pie chart and bar chart below. No child in either year had more than 5 pets.
There are 36 children in year 5.
One child is chosen at random from all the children in year 5 and year 6.
What is the probability that this child has no more than 1 pet?
Some letters are made using only straight lines e.g. T.
Some letters are made using straight lines and curved lines e.g. P. Some letters are made using only curved lines e.g. S. Six cards spell out the name BANGOR.
In a game, the six cards are placed in a bag. One card is chosen at random. The letter on the card is noted and the card is returned to the bag. If the card has a letter on it that is made using only straight lines, the player gains 10 points. A card with any other type of letter gains no points. Leah plays the game 24 times. Do you expect Leah to score a total of 100 points?
You must show all your working.
A company has two sites.
One is in North Wales and the other is in South Wales.
The pie charts below show the distribution of its 96 part-time staff and its 150 full-time staff.
A person is chosen at random from the company’s 246 staff members.
What is the probability that this person works at the site in North Wales?
A company has two sites.
One is in North Wales and the other is in South Wales.
The pie charts below show the distribution of its 96 part-time staff and its 150 full-time staff.
A person is chosen at random from the company’s 246 staff members.
What is the probability that this person works at the site in North Wales?
Dyfrig has a bag containing identically-sized coloured balls. There are ten black balls and ten green balls in the bag.
Dyfrig adds red balls to the bag.
Now, when Dyfrig selects a ball at random, there is an even chance of selecting a red ball.
How many red balls did Dyfrig add to the bag?
A game uses 15 coloured cards.
There are: • 5 red (R) cards numbered 1 to 5, • 5 yellow (Y) cards numbered 1 to 5, • 5 pink (P) cards numbered 1 to 5.
The cards are all placed in a box. One card is chosen at random from the box.
The grid below is used to show all the possible outcomes. Fill in all the spaces with a label or an outcome.
Some of the spaces have already been filled in.
What is the probability that the card chosen at random is a pink card showing a number
greater than 3?
A group of pupils is asked whether they can speak Welsh, French, both languages, or neither language.
Their answers are shown in the Venn diagram below. The universal set, 
, contains all the pupils in the group.
How many of the pupils cannot speak French?
One pupil from the group is chosen at random.
What is the probability that this pupil can speak both Welsh and French?
A group of pupils is asked whether they can speak Welsh, French, both languages, or neither language.
Their answers are shown in the Venn diagram below. The universal set, 
, contains all the pupils in the group.
How many of the pupils cannot speak French?
One pupil from the group is chosen at random.
What is the probability that this pupil can speak both Welsh and French?
A biased coin is thrown 100 times. The number of heads thrown is recorded after 20 throws, 40 throws, 60 throws, 80 throws and 100 throws.
Some of the results are recorded in the relative frequency table below.
Complete the table.
| Number of throws | 20 | 40 | 60 | 80 | 100 |
| Number of heads | 11 | 18 | 24 | 30 | |
| Relative frequency | 0·55 | 0·45 | 0·375 | 0·37 |
The pie chart below shows the favourite sport of 60 people.
Which is the modal sport?
One person is chosen at random.
What is the probability that this person said swimming is their favourite sport?
How many people said tennis is their favourite sport?
Twenty-five balls have numbers printed on them.
Some of the balls are coloured yellow (Y), the others are coloured blue (B). The list below shows both the colour of each ball and the number printed on it.
Y 76 Y 217
B 54 B 126
Y 21 Y 438
Y 32 B 561
B 194
Y 69 B 37 B 518
Y 94 Y 157
Y 208 Y 382
B 56 B 234
Y 72 B 84 Y 68 Y 271
Y 53 B 100
Y 321
Complete the frequency table.
How can you use your table to check that all the balls have been counted?
The 25 balls are placed in a box. One ball is chosen at random.
What is the probability that it is a yellow ball numbered less than 100?
Twenty-five balls have numbers printed on them.
Some of the balls are coloured yellow (Y), the others are coloured blue (B). The list below shows both the colour of each ball and the number printed on it.
Y 76 Y 217
B 54 B 126
Y 21 Y 438
Y 32 B 561
B 194
Y 69 B 37 B 518
Y 94 Y 157
Y 208 Y 382
B 56 B 234
Y 72 B 84 Y 68 Y 271
Y 53 B 100
Y 321
Complete the frequency table.
How can you use your table to check that all the balls have been counted?
The 25 balls are placed in a box. One ball is chosen at random.
What is the probability that it is a yellow ball numbered less than 100?
The Anglesey Show is a two-day event held every August.
On the second day a random sample of 3000 visitors at the show were asked the same question. The relative frequency of those who answered ‘Yes’ on this day was 0·42. Calculate the relative frequency of those who said they lived on Anglesey when the samples for both days were combined.
Give your answer as a decimal.
Which of the following is most likely to give the best estimate for the relative frequency of visitors to the show living on Anglesey? Circle your answer.
You must give an explanation for your choice.
A company has 3 sites based in Wales.
One is in Carno, one is in Holyhead and one is in Porth.
The pie charts below show the distribution of its 128 female staff and 72 male staff.
A person is chosen at random from the company’s 200 staff members.
What is the probability that this person works at the Porth site?
The Anglesey Show is a two-day event held every August.
On the first day, a random sample of 2000 visitors at the show were asked:
640 of them answered 'Yes'. What was the relative frequency of those who answered ‘Yes’?
Give your answer as a decimal.
On the second day a random sample of 3000 visitors at the show were asked the same question. The relative frequency of those who answered ‘Yes’ on this day was 0·42. Calculate the relative frequency of those who said they lived on Anglesey when the samples for both days were combined.
Give your answer as a decimal.
Which of the following is most likely to give the best estimate for the relative frequency of visitors to the show living on Anglesey? Circle your answer.
You must give an explanation for your choice.
A company has 3 sites based in Wales.
One is in Carno, one is in Holyhead and one is in Porth.
The pie charts below show the distribution of its 128 female staff and 72 male staff.
A person is chosen at random from the company’s 200 staff members.
What is the probability that this person works at the Porth site?
Jane has a different set of cards. These are Jane’s cards.
Jane chooses a card at random from her set of cards. On the probability scale below, mark the points A and B where:
A is the probability of Jane choosing a number less than 10,
B is the probability of Jane choosing the number 15.
A box contains five identical balls numbered 1 to 5 respectively.
One ball is chosen at random from the box. Its number is recorded and the ball is replaced in the box.
This process was carried out 75 times in total.
How many times would you expect an even-numbered ball to have been chosen?
You must show all your working.
Two fair spinners are divided into quarters as shown below.
One spinner shows the values 10, 20, 30 and 40. The other spinner shows the values 1, 2, 3 and 4.
The two spinners are spun and the values shown are added together to form a number. For example, the diagram above would form the number 31.
Consider all the possible numbers that can be formed. Calculate the probability that the spinners will form a number that is a multiple of 7.
You must show all your working in order to justify your answer.
How many ‘sixes’ were thrown in the first 600 throws of the dice?
How many more ‘sixes’ were recorded for these 600 throws than you would expect
when a fair six-sided dice is thrown 600 times?
Two fair spinners are divided into quarters as shown below.
One spinner shows the values 10, 20, 30 and 40. The other spinner shows the values 1, 2, 3 and 4.
The two spinners are spun and the values shown are added together to form a number. For example, the diagram above would form the number 31.
Consider all the possible numbers that can be formed. Calculate the probability that the spinners will form a number that is a multiple of 7.
You must show all your working in order to justify your answer.
How many ‘sixes’ were thrown in the first 600 throws of the dice?
How many more ‘sixes’ were recorded for these 600 throws than you would expect
when a fair six-sided dice is thrown 600 times?
A bag contains a number of different coloured balls.
A ball is selected at random from the bag. The probability of selecting a blue ball is 0.3.
Why is the following statement incorrect?
Explain your answer clearly.
‘More than half the balls in the bag are blue.’
What is the probability that a ball selected at random from the bag is not blue?
There are 50 balls in the bag.
How many of them are blue?
30 rugby supporters travel to Cardiff on a coach. They decide to investigate how many of them can sing one, or both, of the songs ‘Hen Wlad fy Nhadau’ and ‘Bread of Heaven’.
• 12 say they can sing both songs. • 18 say they can sing ‘Bread of Heaven’. • 5 say they cannot sing either of the songs.
Complete the Venn diagram below to show this information.
The universal set, 
, contains all of the 30 supporters on the coach.
One of these supporters is chosen at random.
What is the probability that this person can sing ‘Hen Wlad fy Nhadau’?
A travel company offers the following holiday options.
List all the possible different combinations of holiday options that the company offers.
One has been done for you.
Summer Cottage Train
30 rugby supporters travel to Cardiff on a coach. They decide to investigate how many of them can sing one, or both, of the songs ‘Hen Wlad fy Nhadau’ and ‘Bread of Heaven’.
• 12 say they can sing both songs. • 18 say they can sing ‘Bread of Heaven’. • 5 say they cannot sing either of the songs.
One of these supporters is chosen at random.
What is the probability that this person can sing ‘Hen Wlad fy Nhadau’?
Sara is in charge of a game at her school’s Christmas party.
Two fair spinners are spun as shown in the example below.
People can make a two-digit number using the numbers shown on the spinners using the following rule:
Multiply the number on the first spinner by 10 and then add the number on the second spinner.
One example, as shown above, makes the number 21, because 2 × 10 + 1 = 21.
How many different numbers can be made playing this game?
Write down all the prime numbers that can be made playing this game.
What is the probability that a person makes a prime number when playing the game
once?
Sara charges each person £1 to play the game once. Each player who makes a prime number from their spins wins £2.
How much profit would the school expect to make when 180 people play the game?
The following cards spell out the name Ystradgynlais.
In an experiment, the cards are turned face down and rearranged. A card is selected at random and the letter on the card is recorded.
The experiment is carried out 325 times.
How many times would you expect the letter Y to be recorded?
Blues, Dragons, Ospreys and Scarlets are four Welsh rugby teams.
Aled asked a group of 170 pupils which of these 4 teams they preferred. He then drew this bar chart to show the data that he had collected.
Aled knew that 50 of these pupils said that they preferred the Blues.
Complete the table below.
| Rugby team preferred | Number of pupils |
| Blues | 50 |
| Dragons | |
| Ospreys | |
| Scarlets |
A pupil is chosen at random from this group.
What is the probability that this pupil preferred the Blues?
A fair, six-sided dice is rolled. What is the probability that a 4 is shown on the dice?
Circle your answer.
50 raffle tickets were sold at a charity event. Sian has a 20% chance of winning the top prize. How many tickets did Sian buy?
Circle your answer.
1 2 4 10 20
A bag contains a mixture of blue beads, yellow beads and pink beads. One bead is taken at random from the bag. The probability that the bead is pink is. 
Which of the following sets of beads could have been in the bag?
Circle your answer.
A fair, six-sided dice is rolled. What is the probability that a 4 is shown on the dice?
Circle your answer.
50 raffle tickets were sold at a charity event. Sian has a 20% chance of winning the top prize. How many tickets did Sian buy?
Circle your answer.
1 2 4 10 20
A bag contains a mixture of blue beads, yellow beads and pink beads. One bead is taken at random from the bag. The probability that the bead is pink is. Which of the following sets of beads could have been in the bag?
Circle your answer.
Also involves Systematic listing and the product rule for counting
David, Jane and Mary are beach inspectors.
Three beaches, Harlech, Rhyl and Porthcawl, are all to be inspected on a certain day. It is decided to share the work so that the inspectors will visit one beach each, chosen at random.
List all the possible different ways they could share the work.
One has been done for you.
David 
Harlech, Jane 
Rhyl and Mary Porthcawl
What is the probability that one of the female inspectors will visit Rhyl?
A group of 20 people visited Anglesey for a weekend break.
• 10 of the group visited Beaumaris Castle. • 13 of the group visited South Stack Lighthouse. • 4 of the group did not visit either of these places.
Complete the Venn diagram below to show this information.
The universal set, 
, contains all of the 20 people in the group.
One person is chosen at random from the group.
What is the probability that this person visited only one of the two places?
A dice is thrown 50 times.
The number shown on the dice is recorded after each throw. The table below shows the results recorded.
| Number shown on dice | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 9 | 7 | 8 | 7 | 6 | 13 |
The relative frequency of throwing a 1 was calculated as 
= 0.18. What was the relative frequency of throwing a 6?
Give your answer as a decimal.
The number 4 was thrown 7 times in the first 50 throws. Using this fact, calculate how many times you would expect a 4 to be thrown when this
dice is thrown 3000 times.
How many times would you expect a 4 to be thrown when a fair dice is thrown 3000
times?
A group of 20 people visited Anglesey for a weekend break.
• 10 of the group visited Beaumaris Castle. • 13 of the group visited South Stack Lighthouse. • 4 of the group did not visit either of these places.
Complete the Venn diagram below to show this information.
The universal set, , contains all of the 20 people in the group.
One person is chosen at random from the group.
What is the probability that this person visited only one of the two places?
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