Year 12 probability and the binomial distribution test to download as PDF

This Year 12 probability and the binomial distribution test lasts 60 minutes and is marked out of 20. It covers the whole chapter for pupils aged 16-17, and the full answers are on a separate page.

⏱️ Duration : 60 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Venn diagram and conditional probability
\(P(A)=0.6\), \(P(B)=0.5\) and \(P(A\cup B)=0.8\).
1. Find \(P(A\cap B)\). (2 marks)
2. Find \(P(B|A)\) and state whether \(A\) and \(B\) are independent. (2 marks)
Question 2 – Tree diagram
A box has 4 white and 6 black balls. Two are drawn without replacement. Find the probability that they are the same colour.
Question 3 – Binomial probability
\(X\sim B(10,0.2)\). Find (a) \(P(X=3)\) and (b) \(P(X\ge2)\).
Question 4 – Expected values
A fair coin is tossed 50 times. Let \(X\) be the number of heads.
1. State the distribution of \(X\) and find its mean and variance. (2 marks)
2. Find the probability of exactly 25 heads. (2 marks)
Question 5 – Problem: a spinner
A spinner lands on blue with probability 0.15. It is spun 12 times.
1. Find the probability that blue occurs at least once. (2 marks)
2. Find the probability that blue occurs exactly twice. (1 mark)
3. How many spins are needed so that the probability of at least one blue exceeds 0.95? (1 mark)

How to use this Year 12 probability and the binomial distribution test

First, revise with the probability and the binomial distribution lesson and the worksheet. Then sit the test in one go, with a timer set to 60 minutes. After that, mark your work with the probability and the binomial distribution test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 12 probability and the binomial distribution test as a PDF and print it like a real exam paper. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.

Probability and the binomial distribution – Year 12 A level maths test to download as PDF

Question 1 – Venn diagram and conditional probability

Question 2 – Tree diagram

Question 3 – Binomial probability

Question 4 – Expected values

Question 5 – Problem: a spinner

How to use this Year 12 probability and the binomial distribution test

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