WJEC GCSE Maths
Topic questions Statistics The probability scale
80 questions · 337 marks · about 7.5 hours
Eight cards with numbers on them are shown below.
Jo has four of these cards in her hand.
Dafydd chooses one of Jo’s four cards at random.
• There is an even chance that the number on the card is a square number.
• It is unlikely that the number on the card is a factor of 21.
Which four cards could Jo have in her hand?
Write the numbers on the four cards below.
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.
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?
Cerys chooses a card at random from three different sets of four cards.
In each part, write numbers on the four cards to make the statement true.
It is impossible that the card Cerys chooses will be a 7.
It is likely that the card Cerys chooses will be a 7.
There is an even chance that Cerys chooses a number less than 7.
Find the probability that Evan and Jane both hit the centre of the target.
A bag contains 3 red counters, 5 blue counters and 7 yellow counters.
Sali takes three counters at random from the bag. These counters are not replaced.
Calculate the probability that at least two of the counters are the same colour.
Matilda asked 10 of her friends which was their favourite sport.
They each chose one of rugby, hockey or cricket. Matilda showed the results of her survey in the bar chart below.
Matilda chooses one of her friends at random.
Describe the chance that the friend’s favourite sport is cricket.
Circle the best expression from those below.
impossible unlikely an even chance likely certain
Describe the chance that the friend’s favourite sport is rugby.
Circle the best expression from those below.
impossible unlikely an even chance likely certain
A children’s play area contains a large number of coloured balls.
Some are yellow, some are red, some are blue and the others are pink.
A ball is chosen at random from the play area.
Complete the table below to find the probability of choosing a pink ball.
| Colour | Yellow | Red | Blue | Pink |
| Probability | 0·54 | 0·12 | 0·25 |
There are 575 blue balls in the play area.
What is the total number of balls in the play area?
A group of people hired two buses, Bus A and Bus B, to take them home from a party.
Bus A left the party at 11:00 p.m. Bus B left the party at midnight.
A person from the group is chosen at random. The probability that this person left the party on Bus A is 
. The probability that this person sat on the left-hand side of the bus is equal to the probability that this person sat on the right-hand side.
Complete the following tree diagram.
What is the probability that this person sat on the right-hand side of the bus that left at
midnight?
A children’s play area contains a large number of coloured balls.
Some are yellow, some are red, some are blue and the others are pink.
A ball is chosen at random from the play area.
Complete the table below to find the probability of choosing a pink ball.
| Colour | Yellow | Red | Blue | Pink |
| Probability | 0·54 | 0·12 | 0·25 |
There are 575 blue balls in the play area.
What is the total number of balls in the play area?
A group of people hired two buses, Bus A and Bus B, to take them home from a party.
Bus A left the party at 11:00 p.m. Bus B left the party at midnight.
A person from the group is chosen at random. The probability that this person left the party on Bus A is 
. The probability that this person sat on the left-hand side of the bus is equal to the probability that this person sat on the right-hand side.
Complete the following tree diagram.
What is the probability that this person sat on the right-hand side of the bus that left at
midnight?
Anna has 34 animals on her farm.
She has 10 goats, 20 sheep and 4 cows. Anna chooses one of these 34 animals at random.
There are many socks in a drawer.
The socks are red, green, blue or pink.
A sock is chosen at random from the drawer.
Complete the table below.
| Colour | Red | Green | Blue | Pink |
| Probability | 0·3 | 0·1 | 0·25 |
In the drawer, there are 20 pink socks.
How many red socks are there in the drawer?
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.
There are many socks in a drawer.
The socks are red, green, blue or pink.
A sock is chosen at random from the drawer.
Complete the table below.
| Colour | Red | Green | Blue | Pink |
| Probability | 0·3 | 0·1 | 0·25 |
In the drawer, there are 20 pink socks.
How many red socks are there in the drawer?
Beti walks her dog to a local park and back home every day.
She can either walk along a footpath or along a pavement at the side of a road. The probability that Beti walks to the park along the footpath is 
The probability that Beti walks home from the park along the road is 
Her decisions on which routes to walk to and from the park are independent of each other.
Complete the tree diagram below.
Find the probability that Beti walks to and from the park along the footpath.
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.
Beti walks her dog to a local park and back home every day.
She can either walk along a footpath or along a pavement at the side of a road. The probability that Beti walks to the park along the footpath is 
The probability that Beti walks home from the park along the road is 
Her decisions on which routes to walk to and from the park are independent of each other.
Complete the tree diagram below.
Find the probability that Beti walks to and from the park along the footpath.
Calculate the probability that every child passes their ball to the left.
Calculate the probability that one of the three children does not receive a ball.
Catrin has a bag containing only apples, bananas and lemons. She has 20 pieces of fruit altogether in her bag. Catrin chooses one piece of fruit at random from her bag.
The probability that she chooses each type of fruit is shown on the probability scale below, where • A represents apple • B represents banana • L represents lemon.
How many apples does Catrin have in her bag?
Whitney walks, cycles or travels on the bus to work each day.
On any randomly chosen day: • the probability that she walks to work is 0·25 • the probability that she cycles to work is 0·45.
At work, the probability that there will be a fire drill on any randomly chosen day is 0·04.
How Whitney travels to work is independent of whether or not there is a fire drill.
Complete the tree diagram shown below.
On a randomly chosen day, what is the probability that Whitney walks to work and there
is a fire drill?
A large number of prize tokens are placed in a box.
The tokens are identical in shape and size.
Gold, Silver, Bronze or No Prize is written on each token.
One token is chosen at random from the box. The table below shows the probability of choosing a Gold prize token and the probability of choosing a Silver prize token.
| Token | Gold | Silver | Bronze | No Prize |
| Probability | 0·02 | 0·18 |
There are three times as many No Prize tokens in the box as there are Bronze prize tokens.
Complete the table.
There are 15 Gold prize tokens in the box.
How many Silver prize tokens are there in the box?
Whitney walks, cycles or travels on the bus to work each day.
On any randomly chosen day: • the probability that she walks to work is 0·25 • the probability that she cycles to work is 0·45.
At work, the probability that there will be a fire drill on any randomly chosen day is 0·04.
How Whitney travels to work is independent of whether or not there is a fire drill.
Complete the tree diagram shown below.
On a randomly chosen day, what is the probability that Whitney walks to work and there
is a fire drill?
A large number of prize tokens are placed in a box.
The tokens are identical in shape and size.
Gold, Silver, Bronze or No Prize is written on each token.
One token is chosen at random from the box. The table below shows the probability of choosing a Gold prize token and the probability of choosing a Silver prize token.
| Token | Gold | Silver | Bronze | No Prize |
| Probability | 0·02 | 0·18 |
There are three times as many No Prize tokens in the box as there are Bronze prize tokens.
Complete the table.
There are 15 Gold prize tokens in the box.
How many Silver prize tokens are there in the box?
Catherine has three spinners, as shown below.
She spins each spinner once.
Calculate the probability that all three spinners land on prime numbers.
The numbers that the three spinners land on are added together.
Calculate the probability that the total is greater than 4.
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.
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?
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?
Bag A and Bag B contain only red and blue balls.
The probability of choosing a red ball from Bag A is 
. The probability of choosing a red ball from Bag B is 0∙25.
A ball is chosen at random from each bag.
Complete the tree diagram below.
Find the probability that the two balls chosen are the same colour.
Bag A and Bag B contain only red and blue balls.
The probability of choosing a red ball from Bag A is 
. The probability of choosing a red ball from Bag B is 0∙25.
A ball is chosen at random from each bag.
Complete the tree diagram below.
Find the probability that the two balls chosen are the same colour.
Tim chooses one letter at random from the word TOMATO.
Describe the chance that Tim chooses the letter T.
Circle the correct expression from those given below.
impossible unlikely an even chance likely certain
Megan chooses one letter at random from the word BANANA.
Describe the chance that Megan chooses the letter A.
Circle the correct expression from those given below.
impossible unlikely an even chance likely certain
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.
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.
A and B are independent events.
The probability of event A occurring is 0·6. The probability of event A and event B occurring is 0·48.
Calculate the probability of neither event A nor event B occurring.
A and B are independent events.
The probability of event A occurring is 0·6. The probability of event A and event B occurring is 0·48.
Calculate the probability of neither event A nor event B occurring.
A bag contains 10 balls. 5 of the balls are blue, 4 of the balls are red and 1 ball is green. Three balls are chosen at random, one at a time, without replacement.
Calculate the probability that the first ball is blue, the second ball is red and the third ball is green.
You must show all your working.
Calculate the probability that at least one blue ball is chosen.
You must show all your working.
A card is chosen at random from a set of four cards.
In each question, write numbers on the four cards to make each of the following statements true.
It is certain that the chosen card will be a 5.
It is an even chance that the chosen card will be a 3.
It is unlikely that the chosen card will be a 2.
Also involves Probability experiments and frequency
Geraint is running a game in a school fair. A large number of balls are placed in a box. Each of the balls is one of three colours: bronze, silver or gold. In the game, a ball is chosen at random from the box. The table below shows the probability of choosing a bronze ball and the probability of choosing a silver ball.
| Colour | Bronze | Silver | Gold |
| Probability | 0·68 | 0·22 |
In the game, each person pays £2 to choose a ball at random from the box. The ball is then returned to the box.
The person wins £3 if a silver ball is chosen. The person wins £8 if a gold ball is chosen. There is no prize for choosing a bronze ball.
100 people each play the game once.
How much profit would you expect Geraint to make?
You must show all your working.
A group of people have put their names forward to carry the Welsh flag at a sporting event.
Each person lives in North Wales, Mid Wales or South Wales.
One person from the group is chosen at random. The probability of choosing a person who lives in North Wales is 0·3. The probability of choosing a person who lives in Mid Wales is 0·25.
The probability of choosing a person who is under 18 years old is 0·2.
The people’s ages are independent of where they live.
What is the probability of choosing a person who lives in South Wales and is under
18 years old?
Geraint is running a game in a school fair. A large number of balls are placed in a box. Each of the balls is one of three colours: bronze, silver or gold. In the game, a ball is chosen at random from the box. The table below shows the probability of choosing a bronze ball and the probability of choosing a silver ball.
| Colour | Bronze | Silver | Gold |
| Probability | 0·68 | 0·22 |
In the game, each person pays £2 to choose a ball at random from the box. The ball is then returned to the box.
The person wins £3 if a silver ball is chosen. The person wins £8 if a gold ball is chosen. There is no prize for choosing a bronze ball.
100 people each play the game once.
How much profit would you expect Geraint to make?
You must show all your working.
A group of people have put their names forward to carry the Welsh flag at a sporting event.
Each person lives in North Wales, Mid Wales or South Wales.
One person from the group is chosen at random. The probability of choosing a person who lives in North Wales is 0·3. The probability of choosing a person who lives in Mid Wales is 0·25.
The probability of choosing a person who is under 18 years old is 0·2.
The people’s ages are independent of where they live.
What is the probability of choosing a person who lives in South Wales and is under
18 years old?
Three of the seven cards shown above are selected at random, without being replaced.
Find the probability that the first card selected is a 3, the second is a 4 and the third is
a 5.
Find the probability that the sum of the numbers selected is greater than 9.
80 cards are placed in a box. Each card shows a picture of one of four islands near the coast of Wales: Bardsey Island, Ramsey Island, Skomer Island or Puffin Island.
A card is chosen at random from the box. The table below gives some of the probabilities that the chosen card shows a picture of a particular island.
| Island | Bardsey Island (Ynys Enlli) | Ramsey Island (Ynys Dewi) | Skomer Island (Ynys Sgomer) | Puffin Island (Ynys Seiriol) |
| Probability | 0·4 | 0·15 | 0·25 |
How many of the 80 cards show a picture of Puffin Island?
You must show all your working.
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?
Alice works for an engineering company.
A working day is chosen at random. From keeping a record over the last year, Alice knows that, for this working day,
• the probability that she travels to work by car is 0·7, • the probability that she arrives at work before 8:00 a.m. is 0·4, • her time of arrival is independent of how she travels to work.
Using the above information, draw and fully label a complete tree diagram.
You must include all probabilities.
What is the probability that, on the randomly-chosen working day, Alice travels to work by
car and arrives before 8:00 a.m.?
Alice works for an engineering company.
A working day is chosen at random. From keeping a record over the last year, Alice knows that, for this working day,
• the probability that she travels to work by car is 0·7, • the probability that she arrives at work before 8:00 a.m. is 0·4, • her time of arrival is independent of how she travels to work.
Using the above information, draw and fully label a complete tree diagram.
You must include all probabilities.
What is the probability that, on the randomly-chosen working day, Alice travels to work by
car and arrives before 8:00 a.m.?
Dewi has a box containing eleven socks.
Six of the socks are red, four are green and one is yellow.
Early one morning, without switching on the light, Dewi selects two socks at random.
Calculate the probability that the first sock selected is yellow and the second is red.
Calculate the probability that Dewi selects two socks of the same colour.
Calculate the probability that at least one green sock is selected.
Sara has 20 balls in a bag. There are 15 blue balls and 5 red balls. Sara chooses a ball at random from her bag.
Describe the chance that Sara chooses a red ball from her bag.
Circle the correct expression from those given below.
impossible unlikely an even chance likely certain
Gareth has some cards with a number written on each one. These are Gareth’s cards.
Gareth chooses one of his cards at random.
Describe the chance that Gareth chooses a card with an odd number on it.
Circle the correct expression from those given below.
impossible unlikely an even chance likely certain
200 young people are taking part in a conference held at Aberystwyth.
One of the young people is chosen at random to be the chairperson.
Complete the table below to find the probability that the person chosen lives outside the
United Kingdom (UK).
| North Wales | Mid Wales | South Wales | Elsewhere in the UK | Outside the UK | |
| Probability | 0·2 | 0·3 | 0·25 | 0·15 |
How many of the 200 young people live in Mid Wales?
200 young people are taking part in a conference held at Aberystwyth.
One of the young people is chosen at random to be the chairperson.
Complete the table below to find the probability that the person chosen lives outside the
United Kingdom (UK).
| North Wales | Mid Wales | South Wales | Elsewhere in the UK | Outside the UK | |
| Probability | 0·2 | 0·3 | 0·25 | 0·15 |
How many of the 200 young people live in Mid Wales?
Dylan is having a weekend break in Wrexham.
The probability that he will visit Erddig Gardens is 0·7. The probability of Dylan going to the Bersham Heritage Centre is independent of him visiting Erddig Gardens.
The probability that he visits Erddig Gardens and goes to the Bersham Heritage Centre is 0·28.
Complete the following tree diagram.
Calculate the probability that Dylan visits Erddig Gardens but does not go to the Bersham
Heritage Centre.
Also involves Fractions, decimals and percentages
Dylan is having a weekend break in Wrexham.
The probability that he will visit Erddig Gardens is 0·7. The probability of Dylan going to the Bersham Heritage Centre is independent of him visiting Erddig Gardens.
The probability that he visits Erddig Gardens and goes to the Bersham Heritage Centre is 0·28.
Complete the following tree diagram.
Calculate the probability that Dylan visits Erddig Gardens but does not go to the Bersham
Heritage Centre.
The following twelve cards are placed in a box.
Three cards are chosen at random from the box at the same time.
Calculate the probability that the three cards drawn are all the letter ‘C’.
The letters A, E and O are vowels. All the other letters on these cards are consonants.
Calculate the probability that the three cards drawn include at least one consonant and at
least one vowel.
Leah is visiting Cardiff.
The probability that she will go on a tour bus is 0·3. The probability of Leah seeing a show at the Millennium Centre is independent of her going on a tour bus.
The probability that she goes on a tour bus and sees a show at the Millennium Centre is 0·24.
Complete the following tree diagram.
Calculate the probability that Leah does not go on a tour bus and does not see a show at
the Millennium Centre.
Leah is visiting Cardiff.
The probability that she will go on a tour bus is 0·3. The probability of Leah seeing a show at the Millennium Centre is independent of her going on a tour bus.
The probability that she goes on a tour bus and sees a show at the Millennium Centre is 0·24.
Complete the following tree diagram.
Calculate the probability that Leah does not go on a tour bus and does not see a show at
the Millennium Centre.
A box contains 4 yellow cards and 6 red cards.
Three cards are chosen at random, one at a time, without replacement.
Calculate the probability that the first two cards are yellow and the third card is red.
You must show all your working.
Calculate the probability that at least one yellow card is chosen.
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.
Alwena regularly travels from Anglesey to Cardiff to attend meetings.
For each meeting, she chooses one of three ways to travel: by plane, train or car. The probability of a meeting being held on a Saturday is 0.08. The probability that Alwena travels by plane to a meeting is 0.15. The probability that she travels by train is 0.45. Her decision on how to travel is independent of the day on which the meeting is held.
Complete the following tree diagram.
A meeting is chosen at random. Calculate the probability that the meeting is held on a Saturday and that Alwena travels
by plane or by car.
Alwena regularly travels from Anglesey to Cardiff to attend meetings.
For each meeting, she chooses one of three ways to travel: by plane, train or car. The probability of a meeting being held on a Saturday is 0.08. The probability that Alwena travels by plane to a meeting is 0.15. The probability that she travels by train is 0.45. Her decision on how to travel is independent of the day on which the meeting is held.
Complete the following tree diagram.
A meeting is chosen at random. Calculate the probability that the meeting is held on a Saturday and that Alwena travels
by plane or by car.
Mai has a box of 60 different beads. There are 40 red beads in the box. Mai chooses a bead at random from the box.
Describe the chance that Mai chooses a red bead.
Circle the correct expression from those given below.
impossible unlikely an even chance likely certain
Ifan has a box of 12 cakes. There are 6 chocolate cakes and the rest are lemon cakes. Ifan chooses a cake at random from the box.
Describe the chance that Ifan chooses a lemon cake.
Circle the correct expression from those given below.
impossible unlikely an even chance likely certain
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.
There are 50 balls in the bag.
How many of them are blue?
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
A holiday is chosen at random from all the different combinations on offer. P is the probability that the chosen holiday is a
Summer holiday, staying in a Cottage and travelling by Train.
Mark the point P on the probability scale shown below.
0 1
A box contains many discs, identical in shape and size.
A picture of one of four Welsh castles is printed on each disc.
A disc is chosen at random from the box. Complete the table below to find the probability of choosing a disc showing Dinefwr
In the box, there were 522 discs showing a picture of Caernarfon Castle.
How many of the discs showed a picture of Harlech Castle?
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?
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
A box contains many discs, identical in shape and size.
A picture of one of four Welsh castles is printed on each disc.
A disc is chosen at random from the box. Complete the table below to find the probability of choosing a disc showing Dinefwr
In the box, there were 522 discs showing a picture of Caernarfon Castle.
How many of the discs showed a picture of Harlech Castle?
Complete the tree diagram shown below.
Gender Transport
The person chosen at random receives a gift voucher. What is the probability that this person is female and travelled up the mountain by train?
Complete the tree diagram shown below.
Gender Transport
The person chosen at random receives a gift voucher. What is the probability that this person is female and travelled up the mountain by train?
All the members of a farming club visited the Royal Welsh Agricultural Show.
They all travelled to the show either by bus or by car. None of them visited the show on more than one day. The decision to travel by car or by bus was independent of the day of the visit.
A member of the club was selected at random. The probability that this member travelled by bus was 0·87. The probability that this member visited the show on the first day was. 
What is the probability that a member, chosen at random, was not one of those who
travelled by bus on the first day of the show?
All the members of a farming club visited the Royal Welsh Agricultural Show.
They all travelled to the show either by bus or by car. None of them visited the show on more than one day. The decision to travel by car or by bus was independent of the day of the visit. A member of the club was selected at random. The probability that this member travelled by bus was 0·87. The probability that this member visited the show on the first day was. 
What is the probability that a member, chosen at random, was not one of those who
travelled by bus on the first day of the show?
Ceri has a set of cards.
Each of her cards is labelled North, East, South or West.
Ceri chooses one card at random from her set of cards. Complete the table below to find the probability of Ceri choosing a card labelled West.
| Label | North | East | South | West |
| Probability | 0.4 | 0.25 | 0.2 |
Ceri chooses one card at random from her set of cards.
What is the probability that the card is labelled East or South?
Sasha has an identical set of cards. Ceri and Sasha each choose one card at random from their set of cards.
What is the probability that they both choose a card labelled North?
100 boxes each contain 10 balls.
45 of the boxes are labelled A. They each contain 7 black balls and 3 white balls.
25 of the boxes are labelled B. They each contain 4 black balls and 6 white balls.
The rest of the boxes are labelled C. They each contain 8 black balls and 2 white balls.
In a game, a player chooses a box at random, and then chooses a ball at random from that box.
Complete the tree diagram shown below.
What is the probability that a player will select a black ball?
If a large number of people played the game, approximately what fraction of them would you expect to choose a white ball?
Circle your answer.
Also involves Fractions
A bag contains 6 red blocks, 4 green blocks and 2 yellow blocks.
Three blocks are taken from the bag, at random, without replacement.
What is the probability that the first block removed is red, the second is green and the
third is yellow?
Calculate the probability that all three blocks will be the same colour.
Write down the probability that the three blocks will not be the same colour.
100 boxes each contain 10 balls.
45 of the boxes are labelled A. They each contain 7 black balls and 3 white balls.
25 of the boxes are labelled B. They each contain 4 black balls and 6 white balls.
The rest of the boxes are labelled C. They each contain 8 black balls and 2 white balls.
In a game, a player chooses a box at random, and then chooses a ball at random from that box.
Complete the tree diagram shown below.
What is the probability that a player will select a black ball?
If a large number of people played the game, approximately what fraction of them would you expect to choose a white ball?
Circle your answer.
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