Probability (Edexcel GCSE Statistics: Foundation): Exam Questions

Zander spins a fair 4‑sided spinner.

Write down the probability that the spinner lands on 1

Zander now spins the spinner 60 times.

Work out the expected number of times the spinner will land on 1

Helen spins a biased 3‑sided spinner 45 times.

On each spin, the spinner can land on 1 or on 2 or on 3

Here are her results.

Helen is going to spin the 3‑sided spinner again.

Use the results in the table to find an estimate that the spinner will land on 2 or on 3

Helen concludes that the 3‑sided spinner is most likely to land on a score of 3 the next time it is spun.

Comment on the reliability of Helen’s conclusion.

and are two events.

The Venn diagram shows information about the probabilities of events related to and happening.

Find

(i) the probability of event happening

(1)

(ii) Find

(1)

(iii) Find .

(2)

Two different events and are independent.

Find .

Carol spins the two spinners and .
She adds their scores together.

Complete the sample space diagram below to show all the possible totals.

Assuming that the spinners are fair, find the probability

(i) that the total score is 3,

(1)

(ii) that the spinners show the same score.

(1)

Carol spins spinner 120 times. The table below shows the scores that she got.

Carol concludes that spinner is biased towards the number 1.

Assess whether or not Carol's conclusion is appropriate.

Kyryl and Matthew play against each other in a game of tennis and a game of squash. In each game either Kyryl or Matthew wins.

The probability that Kyryl wins the game of tennis is 0.35.
The probability that Matthew wins the game of squash is 0.45.

Complete the tree diagram to show this information.

Matthew says that the probability of him winning both games is greater than the probability of Kyryl winning both games.
Is Matthew correct? You must show how you get your answer.

David has 10 cards each with a single letter on it as shown.

A card is picked at random.

Underline the word from the list below that best describes the likelihood that the card has a letter A on it.

impossible     certain     likely     evens     unlikely

Complete this sentence using two different letters.

Cards with the letters .................... and ..................... are equally likely to be picked.

On the probability scale below, mark with a cross (×) the probability that the card has a letter C on it.

On the probability scale below, mark with a cross (×) the probability that the card has a letter A or a letter C on it.

Jenny is investigating how many days per week people use a gym.

She asks the 40 people in her fitness group how often they use the gym each week. Jenny draws this bar chart for her data.

One of these people is chosen at random.

Find the probability that this person uses the gym exactly 2 days per week.

What is the modal number of days to use the gym each week?

Jenny thinks that there are a lot of people in her fitness group who are exercising less than 2 days per week as there is a total of 10 people who used the gym on 0 days or 1 day per week.

Explain why Jenny might not be correct.

Tachi collects data on the heights, in metres, of a sample of Egyptian pyramids.

Here is her data.

(Source: www.rankred.com (opens in a new tab))

Tachi picks one of these pyramids at random.

Find the probability that this pyramid will have a height of more than 100 m.

The mean height of a sample of Mexican pyramids is 53.5 m.

Tachi says, "On average these Egyptian pyramids are twice as high as the Mexican pyramids."

Is Tachi correct?
You must show working to support your answer.

The range of heights for the Mexican pyramids is 45m.
The lowest height of the Mexican pyramids is 30m.

Work out the greatest height of the Mexican pyramids.

............................. m

Khatia organises two different training courses, Course A and Course B, to help people to learn to type.
She wants to compare the two different courses to see which is better.
At the end of each course the people are given a skills test.

The table shows the number of participants who passed and failed the skills test for each of the two courses.

Find the relative risk of failing the skills test having taken Course A compared to Course B.

Give an interpretation of your answer to part (a).

Jonathan has a fair 6-faced dice which has the numbers 1, 2, 3, 4, 5 and 6 on its faces.

Jonathan rolls his dice once.

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

Kasia has a fair 8-faced dice which has the numbers 1, 2, 3, 4, 5, 6, 7 and 8 on its faces.

Choose the word from the list below that best describes the likelihood that the dice lands on a 9

Kasia rolls her dice 80 times.

Work out the number of times you would expect her dice to land on a 5

Jonathan is going to roll his dice once.
Kasia is going to roll her dice once.

Is Jonathan more likely to roll a 6 than Kasia?
You should justify your answer.

The following is an extract from part of a row of a random number list.

68236 35335 71329

Use the random number list to complete the table for the first 5 random 2-digit numbers.

The most common blood type in the United Kingdom is O+

The percentage of people in the United Kingdom with O+ blood type is 38%

Asha uses a simulation method to estimate how many donors would be needed to find exactly 3 donors with O+ blood type.

Asha is going to use the following 2-digit numbers for her simulation.

Explain why this is an appropriate way to allocate the random numbers.

Asha runs trials using her simulation method.
The result of each trial is the number of random numbers used until Asha gets exactly 3 donors with O+ blood type.
The table below shows the results of her first 4 trials.

The set of random numbers used by Asha to complete the fifth trial are shown below.

60   13   12   86   73   10   98   95   43   46

Using this set of random numbers, find the result for the fifth trial.
You must make it clear how you obtain your answer.

Asha finds the mean of her 5 results and decides that the results of her simulation are sufficient to predict the number of donors needed to find at least 3 with O+ blood type in the next blood donation session.

Explain whether the method that Asha uses to predict the number of donors required is appropriate.

A fair 3-sided spinner numbered 1, 2 and 3 and a fair 4-faced dice numbered 1, 2, 3 and 4 are used in a game.

To play the game, a player spins the spinner once and rolls the dice once. The total score is found by adding the number the spinner lands on and the number the dice lands on.

Complete the sample space diagram to show all the possible total scores.

4-faced dice

To win the game a player needs to get a total score of at least 6 Chloe plays the game once.

Find the probability that Chloe does not win the game.

Norbert asked each of the students in his class to name their favourite fruit from Apple, Banana, Orange or Pear.

The results are shown below.

Fill in the tally chart for this information and complete the frequency column.

How many students are in the class?

Find the probability that this student’s favourite fruit is Orange.

Compare the number of students whose favourite fruit is Apple to the number of students whose favourite fruit is Pear.

Norbert decides to find the favourite fruit that is the mode.

Explain why the mode is an appropriate average for Norbert to find for this type of data.

Give one advantage of the tally chart over the raw data.

Norbert wants to draw a diagram to represent his results.

Choose the type of diagram from the list below that is most suitable for him to draw.

Keshav has a spinner with equal sections numbered 1, 2, 3 and 4

To investigate whether or not the spinner is biased towards the number 1 he spins the spinner 40 times.

Explain what is meant by ‘biased towards the number 1’

Here is information about Keshav’s results.

Keshav says the results show that the spinner is biased.

Discuss whether or not the information in the table supports what Keshav says.

What could Keshav do to help improve the accuracy of his investigation?

Linzi is the owner of a coffee shop and makes afternoon teas for customers.

The customers have an option of egg or ham sandwiches and an option of plain or fruit scones.

The incomplete two‑way table shows information about the number of afternoon teas she makes one Saturday

Complete the two‑way table.

Write down the probability that this customer

(i) ordered a plain scone,

[1]

(ii)ordered an egg sandwich and a fruit scone,

[1]

(iii) did not order a ham sandwich.

[2]

Linzi needs to place an order for scones for the next Saturday.

Use the information in the table to help her decide if she should order more fruit scones than plain scones. Give a reason for your answer