University probability and random variables test to download as PDF

This University probability and random variables test lasts 60 minutes and is marked out of 20. It covers the whole chapter for pupils aged 18-19, and the full answers are on a separate page.

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

Mark/20

Question 1 – Independent events
\(A\) and \(B\) are independent with \(P(A)=0.4\) and \(P(B)=0.35\).
1. Find \(P(A\cup B)\). (2 marks)
2. Find \(P(A\mid B^c)\) and \(P(A^c\cap B^c)\). (2 marks)
Question 2 – Two machines
Machine 1 makes 70% of the bolts in a workshop, with 4% defective; machine 2 makes the rest, with 10% defective.
1. Find the probability that a bolt is defective. (2 marks)
2. A bolt is defective. Find the probability that it came from machine 2. (2 marks)
Question 3 – A discrete random variable
\(P(X=1)=0.2\), \(P(X=2)=0.5\), \(P(X=3)=0.3\).
1. Find \(E[X]\) and \(\operatorname{Var}(X)\). (2 marks)
2. Find \(E[5-2X]\) and \(\operatorname{Var}(5-2X)\). (2 marks)
Question 4 – Binomial and Poisson
In a large batch, 10% of light bulbs are faulty. A sample of 20 bulbs is taken.
1. Find the probability of exactly 2 faulty bulbs using \(B(20,0.1)\). (2 marks)
2. Approximate the same probability using a Poisson distribution and comment. (2 marks)
Question 5 – Problem: machined parts
The length of a machined part is \(L\sim N(30,\,0.4^2)\) mm. Parts are accepted if \(29.5\le L\le30.6\).
1. Find the probability that a part is accepted. (2 marks)
2. Parts are packed in boxes of 10. Find the probability that every part in a box is acceptable, and comment on the process. (2 marks)

How to use this University probability and random variables test

First, revise with the probability and random variables 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 random variables test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this University probability and random variables 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 random variables – university Year 1 maths test to download as PDF

Question 1 – Independent events

Question 2 – Two machines

Question 3 – A discrete random variable

Question 4 – Binomial and Poisson

Question 5 – Problem: machined parts

How to use this University probability and random variables test

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