Year 11 conditional probability test to download as PDF

This Year 11 conditional probability test lasts 45 minutes and is marked out of 20. It covers the whole chapter for pupils aged 15-16, and the full answers are on a separate page.

⏱️ Duration : 45 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Two-way table (Higher)
80 students were asked if they like a new canteen menu.
Likes Does not like
Boys 22 18
Girls 26 14
1. Find \(P(\text{girl}\mid\text{likes})\). (2 marks)
2. Find \(P(\text{likes}\mid\text{boy})\). (2 marks)
Question 2 – Tree diagram (Higher)
A bag has 4 green and 6 yellow beads. Two beads are taken without replacement.
1. Find the probability that they are the same colour. (3 marks)
2. Given that the first is yellow, find the probability that the second is green. (1 mark)
Question 3 – Formula (Higher)
\(P(A)=0.6\), \(P(B)=0.5\) and \(P(A\cap B)=0.35\).
1. Find \(P(A\mid B)\). (2 marks)
2. Are \(A\) and \(B\) independent? Show your working. (2 marks)
Question 4 – Backwards probability (Higher)
The probability of rain is 0.25. If it rains, the probability that a bus is late is 0.3. If it does not rain, the probability that the bus is late is 0.1.
1. Find the probability that the bus is late. (2 marks)
2. The bus is late. Find the probability that it rained. (2 marks)
Question 5 – Problem: how many blue counters? (Higher)
A bag has 4 red counters and \(n\) blue counters. Two counters are taken at random without replacement. The probability that both are red is \(\dfrac16\).
1. Show that \(n^2+7n-60=0\). (2 marks)
2. Solve the equation to find \(n\). (2 marks)

	Likes	Does not like
Boys	22	18
Girls	26	14

How to use this Year 11 conditional probability test

First, revise with the conditional probability lesson and the worksheet. Then sit the test in one go, with a timer set to 45 minutes. After that, mark your work with the conditional probability test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 11 conditional probability 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.