Pearson Edexcel GCSE (9-1) · Statistics (1ST0)

Binomial distribution (Higher tier): Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Binomial distribution (Higher tier).

10 questions24 marksFree, no account

Question 1

1 mark

Which of the following terms best describes the likelihood of an event that has a probability of 0.95 on the probability scale?

Question 2

1 mark

The probability of a student passing a math test is 0.75, and the probability of passing a science test is 0.80. Assuming these are independent events, calculate the probability that a student passes only one of the two tests.

Question 3

1 mark

Two groups, Group X and Group Y, are tested for a condition.
- In Group X, 5 out of 100 people have the condition.
- In Group Y, 15 out of 200 people have the condition.
Calculate the relative risk of having the condition in Group Y compared to Group X.

Question 4

1 mark

A fair six-sided die is rolled 120 times.
Calculate the expected frequency of rolling a 4.

Question 5

1 mark

In a town, the probability that a person has a specific allergy is 0.08. In a random sample of 1500 people, calculate the expected frequency of people who have this allergy.

Question 6

2 marks

A fair six-sided die is rolled 120 times.
Calculate the expected frequency of rolling a number greater than 4.

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Question 7

3 marks

A factory inspector tests a batch of 500 light bulbs. The probability that a bulb is defective is 0.015<\/b>.
Calculate the expected frequency<\/b> of defective bulbs in this batch.<\/p>

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Question 8

5 marks

Two events, \(A\) and \(B\), are such that \(P(A) = 0.6\), \(P(B) = 0.5\), and \(P(A \text{ and } B) = 0.2\).
Calculate the probability of \(P(A \text{ or } B)\)<\/b> and determine if events \(A\) and \(B\) are independent<\/b>. Justify your answer with a calculation.<\/p>

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Question 9

4 marks

A fair six-sided die is rolled 120 times. The theoretical probability of rolling a '6' is \(\frac{1}{6}\).

(a) Calculate the expected frequency of rolling a '6' in 120 trials.
(b) In the actual experiment, the '6' was rolled 28 times. Calculate the relative frequency of rolling a '6' based on these results.
(c) State whether the die appears to be biased based on your results, and explain how increasing the number of trials would affect the reliability of this conclusion.

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Question 10

5 marks

A large sports club has 200 members. The following two-way table shows the number of members who play Tennis, Badminton, or both.

Table of Members:
- Plays Tennis only: 85
- Plays Badminton only: 45
- Plays both: 30
- Plays neither: 40

(a) One member is chosen at random. Find the probability that this member plays Badminton. Give your answer as a decimal.
(b) Calculate the probability that a randomly chosen member plays Tennis given that they already play Badminton.
(c) Are the events 'plays Tennis' and 'plays Badminton' independent? Justify your answer using your calculations from (a) and (b).

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