Probability experiments and frequency

Freya has four cards. There is a number on each card.

Freya is going to pick at random one of these cards.

Circle the word in the box below that best describes the likelihood that Freya will pick a card with the number 5 on it.

impossible unlikely evens likely certain

On the probability scale below, mark with a cross (×) the probability that Freya will pick a card with a number less than 6 on it.

Ishani has six cards each with a number on it. Four of these numbers are shown below.

When she picks at random one of the six cards, the probability that she picks a card with

Write a number on each of the blank cards to show one possible set of six cards that Ishani could have.

Some students were asked if they study French (F) or Spanish (S)

The Venn diagram gives information about the results. The values shown represent numbers of students.

How many of these students study only French or only Spanish?

One of these students is chosen at random.

Find the probability that this student studies both French and Spanish.

Here is a biased 5-sided spinner. When the spinner is spun, it can land on blue or on green or on purple or on red or on yellow.

The table gives information about the probability of the spinner landing on each colour.

Sophie spins the spinner once.

Work out the probability that the spinner lands on blue or on green or on purple.

Max spins the spinner 350 times.

Work out an estimate for the number of times the spinner lands on red.

Here is a biased 5-sided spinner. When the spinner is spun, it can land on blue or on green or on purple or on red or on yellow.

The table gives information about the probability of the spinner landing on each colour.

Sophie spins the spinner once.

Work out the probability that the spinner lands on blue or on green or on purple.

Max spins the spinner 350 times.

Work out an estimate for the number of times the spinner lands on red.

Khalid has a box of counters.

17 of the counters are red 28 of the counters are blue the rest of the counters are orange

Khalid is going to take at random a counter from the box. The probability that Khalid will take an orange counter is Work out the number of orange counters that are in the box.

Khalid has a box of counters.

17 of the counters are red 28 of the counters are blue the rest of the counters are orange

Khalid is going to take at random a counter from the box. The probability that Khalid will take an orange counter is Work out the number of orange counters that are in the box.

There are 80 cars in a car park.

27 of the cars are red 10 of the cars are blue the rest of the cars are white

One of the cars in the car park is chosen at random.

Write down the probability that this car is red.

Find the probability that this car is white.

A box contains 10 balls.

5 balls are black 3 balls are green 2 balls are red

Rema is going to take at random a ball from the box.

On the probability scale, mark with a cross () the probability that the ball is black.

On the probability scale, mark with a cross () the probability that the ball is orange.

Johan has three bags of counters, A, B and C He tries to find the probability of taking at random a white counter from each bag. He writes his probabilities in a table.

The probability that Johan writes for bag C is incorrect.

Explain how you know that it is incorrect.

There are 29 cars in a car park.

10 of the cars are red. The rest of the cars are white or blue.

Sasha selects at random one of these cars.

Write down the probability that she selects a red car.

The probability that Sasha selects a white car is

Work out the probability that she selects a blue car.

Here is a biased spinner.

The table gives information about the probability that, when the spinner is spun once, it will land on each number.

Alexis is going to spin the spinner 400 times.

Work out an estimate for the number of times the spinner will land on an odd number.

Here is a biased spinner.

The table gives information about the probability that, when the spinner is spun once, it will land on each number.

Alexis is going to spin the spinner 400 times.

Work out an estimate for the number of times the spinner will land on an odd number.

A biased spinner has three sections each of a different colour.

The table shows the probability that, when the spinner is spun once, it will land on blue or on orange or on white.

Work out the value of x

The spinner is spun 250 times.

Work out an estimate for the number of times the spinner will land on blue.

A bag contains only 10 cent coins and 20 cent coins.

Josip takes at random a coin from the bag, records its value and replaces it in the bag. He then takes at random a second coin from the bag, records its value and replaces it in the bag.

Josip finds the mean value of the two coins. The probability that the two coins have a mean value of 10 cents is Work out the probability that the two coins have a mean value of 15 cents.

The diagram shows a fair spinner with six sections.

Three sections are red, two sections are blue and one section is yellow.

The spinner is spun once.

Write down a word from the box to describe the likelihood that the spinner lands on yellow.

On the probability scale, mark with a cross () the probability that the spinner lands on green.

Here are 8 number cards. 3 of the number cards are blank.

Hugo is going to take at random one of these cards.

Write a number on each of the 3 blank cards so that the probability that Hugo picks a card with an odd number is

There are 30 counters in a bag.

13 of the counters are purple. 11 of the counters are white. The rest of the counters are red.

Suha takes at random a counter from the bag.

Write down the probability that the counter is purple.

Work out the probability that the counter is red.

The counter is put back into the bag.

Clive now puts 10 more counters into the bag. When a counter is taken at random from the bag, the probability that it is white is now

How many of the 10 counters that Clive puts into the bag are white?

Each time Evie plays a game against her computer, she will win or lose.

For each game, the probability that Evie will win is 0.74 Evie is going to play 300 games against her computer.

Work out an estimate for the number of games that Evie will lose.

Moeen has a biased 6-sided dice.

The table gives information about the probability that, when the dice is thrown, it will land on each number.

Show that x + y = 0.19

Given that 3x – y = 0.09

and x + y = 0.19

work out the value of x and the value of y Show clear algebraic working.

Each time Evie plays a game against her computer, she will win or lose.

For each game, the probability that Evie will win is 0.74 Evie is going to play 300 games against her computer.

Work out an estimate for the number of games that Evie will lose.

The diagram shows a fair 6-sided spinner.

Mario spins the arrow on the spinner once.

Write down the word from the box that best describes the likelihood that the arrow will land on

green

yellow

blue

A biased spinner can land on green or on yellow or on brown or on pink.

The table gives the probabilities that, when the spinner is spun, it will land on green or on yellow or on brown.

Timucin spins the spinner 200 times.

Work out an estimate for the number of times the spinner lands on pink.

A biased spinner can land on green or on yellow or on brown or on pink.

The table gives the probabilities that, when the spinner is spun, it will land on green or on yellow or on brown.

Timucin spins the spinner 200 times.

Work out an estimate for the number of times the spinner lands on pink.

Here are 6 counters. Each counter has a number on it.

Finn takes at random one of these counters.

Select with a tick () the word that best describes the likelihood that Finn takes a counter with the number 2 on it.

Select with a tick () the word that best describes the likelihood that Finn takes a counter with the number 3 on it.

Select with a tick () the word that best describes the likelihood that Finn takes a counter with a number greater than 4 on it.

Adam has 8 packets of noodles. Here is the flavour of noodles in each packet.

Adam takes at random a packet of noodles.

On the probability scale, mark with a cross () the probability that Adam takes a packet of Hot and Spicy noodles.

Circle the word that best describes the likelihood that Adam takes a packet of Vegetarian noodles.

Belinda asks 20 people to name the type of rice that they each like the best.

Here are her results.

arborio jasmine basmati jasmine basmati basmati arborio wild jasmine jasmine jasmine jasmine arborio basmati basmati wild basmati jasmine wild arborio

Complete the frequency table for Belinda’s results.

Avner has two fair spinners.

Spinner A
Spinner B

Spinner A can land on 1, 2 or 3 Spinner B can land on 1, 2, 3 or 4

Avner multiplies the number on which spinner A lands by the number on which spinner B lands to find his score.

Complete the table to show all possible scores. Seven of the scores have been completed for you.

Avner spins spinner A once and spinner B once.

Find the probability that his score is an odd number.

Some members of a library were asked to name the type of book that they each liked to read the best.

One of the members is chosen at random. The table shows information about the probability of the type of book that this member answered.

48 members answered comedy books.

Work out how many of the members answered mystery books.

In a bag, there are only red counters, blue counters, green counters and yellow counters.

The total number of counters in the bag is 80

In the bag

the number of red counters is x + 7 the number of blue counters is x – 11 the number of green counters is 3x

Jude takes at random a counter from the bag. The probability that he takes a red counter is

Work out the probability that Jude takes a yellow counter.

The table gives information about the weights, in kg, of the parcels that Pedro delivers on Monday.

Weight (wkg)	Frequency
0 w 2	12
2 w 3	7
3 w 6	15
6 w 9	12
9 w 14	9

On the grid, draw a histogram for this information.

One of the parcels that Pedro delivered on Monday is chosen at random.

Using the information in the table, find an estimate for the probability that this parcel weighs more than 7 kg.

Anjali wants to go on a boat at the seaside.

At the seaside there are 20 boats.

Of these boats 2 are white 5 are blue 7 are green 6 are yellow

Anjali selects at random one of these boats.

Write down the probability that she selects

a green boat,

a white boat or a yellow boat.

Here is a biased 4-sided spinner.

The table gives the probabilities that, when the spinner is spun once, it will land on 1 or it will land on 3

The probability that the spinner will land on 2 is equal to the probability that the spinner will land on 4

Ravina is going to spin the spinner a number of times.

Ravina works out that an estimate for the number of times the spinner will land on 3 is 45

Work out an estimate for the number of times the spinner will land on 4

Here is a biased spinner.

When the spinner is spun once, the probabilities that it lands on red or on yellow or on green are given in the table.

Work out the probability that the spinner lands on red or on yellow.

Yang is going to spin the spinner 300 times.

Work out an estimate for the number of times the spinner will land on purple.

Here is a biased 4-sided spinner.

The table gives the probabilities that, when the spinner is spun once, it will land on 1 or it will land on 3

The probability that the spinner will land on 2 is equal to the probability that the spinner will land on 4

Ravina is going to spin the spinner a number of times.

Ravina works out that an estimate for the number of times the spinner will land on 3 is 45

Work out an estimate for the number of times the spinner will land on 4

Mario is going to play two games on Saturday. He will play one game on Saturday morning and one game on Saturday afternoon.

The following table shows the games from which he is going to choose.

Write down all the possible combinations of games that Mario can play on Saturday.

Mario asked 100 students in his school to name their favourite card game.

His results are shown in the two‑way table below.

One of the students Mario asked is picked at random.

Write down the probability that this student is in Year 11

One of the Year 10 students is picked at random.

Work out the probability that this student did not answer Whist.

4 40 people were asked to name their favourite type of holiday. The pictogram gives information about the number of these people who said each of City Break or Beach or Walking.

How many of these people said Beach?

4 people said Cruise. 9 people said Skiing.

Show this information on the pictogram.

One person from the 40 people asked is selected at random.

Find the probability that this person said City Break.

Bohai works in a shop that sells mobile phones. Last week he sold one mobile phone to each of 300 customers.

The incomplete two‑way table shows some information about these mobile phones.

Complete the two‑way table.

Bohai selects at random one of these 300 customers.

Write down the probability that this customer bought a type B, 64 GB mobile phone.

Bohai now selects at random one of the customers who bought a type A phone last week.

Write down the probability that this customer bought a 128 GB mobile phone.

Each time John plays a game, the probability that he wins the game is 0.65

John is going to play the game 300 times.

Work out an estimate for the number of games that John wins.

A tin contains tea bags with a choice of four different flavours of tea. The four flavours of tea are Assam or Darjeeling or Nilgiri or Rize.

Sara takes at random a tea bag from the tin.

The table shows each of the probabilities that the flavour of the tea Sara takes is Assam or Darjeeling or Rize.

Work out the probability that the flavour of the tea Sara takes is Nilgiri.

Work out the probability that the flavour of the tea Sara takes is either Darjeeling or Rize.

A bag contains only pink sweets, white sweets, green sweets and red sweets.

The table gives each of the probabilities that, when a sweet is taken at random from the bag, the sweet will be green or the sweet will be red.

The ratio number of pink sweets: number of white sweets = 2: 1

There are 28 red sweets in the bag.

Work out the number of white sweets in the bag.

Sandeep is designing some 3‑sided spinners.

He is going to spin each spinner once.

Write a different number on each dotted line so that when the spinner is spun it is impossible that the spinner will land on a number greater than 9

Write a different number on each dotted line so that when the spinner is spun it is certain that the spinner will land on a multiple of 10

The likelihood of an outcome is evens.

On the probability scale, mark with a cross (X) the probability of this outcome.

0 0.5 1

Caroline has a bag containing 10 counters.

In the bag there are

7 red counters 2 blue counters 1 green counter

Caroline is going to choose at random a counter from the bag.

Write down the word from the box that best describes the likelihood that Caroline will take

a red counter,

a yellow counter.

Jamil is going to roll a fair six‑sided dice.

On the probability scale, mark with a cross (X) the probability that the dice will land on an odd number.

On the probability scale, mark with a cross (X) the probability that the dice will land on 2

The two‑way table shows some information about the 60 noodle meals eaten in a noodle bar by each of 60 people last Friday.

Complete the two‑way table.

One of the 60 people is selected at random.

Write down the probability that this person ate Fried Udon noodles.

A bag contains 30 coloured counters. The table gives the number of counters of each colour.

One of the counters is taken at random from the bag.

Write down the probability that this counter is green.

Write down the probability that this counter is not red.

Grace has a fair spinner and a fair dice.

The spinner is 3-sided and can land on 6, 7 or 8 The dice can land on 1, 2, 3, 4, 5 or 6

Grace spins the spinner once and throws the dice once.

Grace subtracts the number that the dice lands on from the number that the spinner lands on to get her score.

Complete the table to show all possible scores. Eight of the scores have been done for you.

Grace spins the spinner once and throws the dice once.

Find the probability that her score is less than 6

Find the probability that her score is an odd number.

There are 12 beads in a bag.

6 of the beads are green 4 of the beads are blue 2 of the beads are pink

Peter takes at random a bead from the bag.

Circle the word in the list below that best describes the likelihood that the bead is green.

impossible unlikely evens likely certain

On the probability scale, mark with a cross (X) the probability that the bead is orange.

On the probability scale, mark with a cross (X) the probability that the bead is blue.

On the probability scale, mark with a cross (X) the probability that the bead is green or pink.

There are 150 people at an international conference. These 150 people were each asked to say what their main method of transport was to get to the conference. The two‑way table shows some information about these people and their answers.

Complete the two‑way table.

One of the men from these 150 people is selected at random.

Write down the probability that this man’s main method of transport was train.

Toy cars are made in a factory. The toy cars are made for 15 hours each day. 5 toy cars are made every 12 seconds.

For the toy cars made each day, the probability of a toy car being faulty is 0.002

Work out an estimate of the number of faulty toy cars that are made each day.

Here are two fair spinners.

Spinner A Spinner B

Chanthira spins each spinner once.

She adds together the number that spinner A lands on and the number that spinner B lands on to find the score.

Complete the table to show all possible scores. Three scores have been done for you.

Find the probability that the score will be 4 or less.

Chanthira now spins both spinners together 84 times.

Find an estimate for the number of times that spinner A and spinner B land on the same number.

Write down all the possible combinations that Mohsen can choose.

Find the probability that Mohsen chooses the red shirt to wear to the party.

There are 20 counters in a bag.

4 of the counters are pink. 9 of the counters are white. The rest of the counters are black.

Jean takes at random one counter from the bag.

Work out the probability that Jean takes a black counter.

The table shows information about the weights, in kilograms, of 40 babies.

Weight (wkg)	Frequency
2 w 3	12
3 w 4	16
4 w 5	9
5 w 6	2
6 w 7	1

Write down the modal class.

Work out an estimate for the mean weight of the 40 babies.

One of the 40 babies is going to be chosen at random.

Find the probability that this baby has a weight of more than 5 kg.

Egor rolled a dice 24 times. Here are his results.

Complete the frequency table for Egor’s results.

Write down the mode of the numbers that Egor rolled.

Egor thinks the dice he rolled is biased.

Give a reason why the results could show that the dice is biased.

Lin has 60 bricks. He puts his 60 bricks into a bag.

Some information about the 60 bricks is shown in the two-way table.

Complete the two-way table.

One of the bricks is taken at random from the bag.

Write down the probability that this brick is blue.

Lin now puts all his large bricks into a sack. He takes at random a large brick from the sack.

Write down the probability that this large brick is orange.

There are 25 pens in a packet. 7 of the pens are green. 10 of the pens are black. The rest of the pens are red. Jurgen takes at random a pen from the packet.

Find the probability that

the pen is black,

the pen is red.

Heidi records the number of packets of pens sold in her shop to each customer last Friday. The table shows information about her results.

Write down the mode of the number of packets.

Work out the total number of packets of pens sold last Friday.

A bag contains only red beads, blue beads, green beads and yellow beads.

The table gives the probabilities that, when a bead is taken at random from the bag, the bead will be blue or the bead will be yellow.

The probability that the bead will be green is twice the probability that the bead will be red.

Sofia takes at random a bead from the bag. She writes down the colour of the bead and puts the bead back into the bag.

She does this 180 times.

Work out an estimate for the number of times she takes a red bead from the bag.

The diagram shows a fair 6-sided spinner.

Rami is going to spin the spinner once.

Circle the word in the box below that best describes the likelihood that the spinner will land on green.

On the probability scale below, mark with a cross (×) the probability that the spinner will land on blue.

On the probability scale below, mark with a cross (×) the probability that the spinner will land on yellow.

Becky has a biased 6-sided dice.

The table gives information about the probability that, when the dice is thrown, it will land on each number.

Becky is going to throw the dice 200 times.

Work out an estimate for the number of times that the dice will land on an even number.

Becky has a biased 6-sided dice.

The table gives information about the probability that, when the dice is thrown, it will land on each number.

Becky is going to throw the dice 200 times.

Work out an estimate for the number of times that the dice will land on an even number.

Each day that Barney goes to college, he either goes by bus or he walks. The probability that Barney will go to college by bus on any day is 0.3

When Barney goes to college by bus, the probability that he will be late is 0.2 When Barney walks to college, the probability that he will be late is 0.1

Complete the probability tree diagram.

Barney will go to college on 200 days next year.

Work out an estimate for the number of days Barney will be late for college next year.

Daniel has five bags of coloured sweets. He picks at random a sweet from each bag. The table shows the probability that the sweet he picks from each bag is red.

From which bag is Daniel least likely to pick a red sweet?

Which bag contains only red sweets?

From which bag is Daniel equally likely to pick a red sweet as a sweet of another colour?

Valentino sells ice cream cones and ice cream tubs. The ice cream flavours are chocolate, strawberry and vanilla.

On Sunday, 120 people each bought one ice cream from Valentino. The two-way table shows some information about these ice creams.

Complete the two-way table.

One of the 120 people is picked at random.

Find the probability that this person bought a vanilla ice cream cone.

Last Thursday, 135 students each bought one item of fruit. The table shows information about the 135 items of fruit they bought.

One of the 135 students is chosen at random.

Find the probability that this student bought an apple or a banana.

A pie chart is drawn for the information in the table.

Work out the size of the angle in the pie chart for oranges.

Javier has two sets of cards. Each set contains 4 cards, one marked A, one marked B, one marked C and one marked D.

Javier is going to take at random one card from each set. The table shows all possible pairs of cards that Javier could take.

Find the probability that Javier will take at least one card marked C.

Javier is going to take at random one card from each set, note the letter on each card and replace the cards.

He is going to do this a total of 80 times.

Work out an estimate for the number of times that Javier will take at least one card marked C.