StudentAid
HomeLearn
9th Class10th Class11th Class12th ClassCambridge past papersBrowse everything
Attendance
Class attendanceVisitor register
For schoolsFor driversFor parentsBook a demo
Learn/ A Level Mathematics/ Past Papers/ 2020/ Feb/March 2020 /Paper 5 (Variant 2)

Probability & Statistics 1 — Variant 2

A Level Mathematics · 9709/52 · Feb/March 2020

Question Paper

PDF · 105 KB · 12 pages

Mark Scheme

PDF · 418 KB · 14 pages

This browser cannot show the PDF inline.

Open the question paper · Open the mark scheme

Questions

5 of 7 questions shown here, checked against the paper. The others are in the PDF above — they contain diagrams or maths we could not yet verify, and we would rather show you the original than a transcription we are not sure of.

1 [3]
The 40 members of a club include Ranuf and Saed. All 40 members will travel to a concert. 35 members will travel in a coach and the other 5 will travel in a car. Ranuf will be in the coach and Saed will be in the car. In how many ways can the members who will travel in the coach be chosen?
2
An ordinary fair die is thrown repeatedly until a 1 or a 6 is obtained.
2(a) [3]
Find the probability that it takes at least 3 throws but no more than 5 throws to obtain a 1 or a 6. On another occasion, this die is thrown 3 times. The random variable XX is the number of times that a 1 or a 6 is obtained.
2(b) [3]
Draw up the probability distribution table for XX.
2(c) [2]
Find E(X)\mathrm{E}(X).
3
The weights of apples of a certain variety are normally distributed with mean 8282 grams. 22% of these apples have a weight greater than 8787 grams.
3(a) [3]
Find the standard deviation of the weights of these apples.
3(b) [4]
Find the probability that the weight of a randomly chosen apple of this variety differs from the mean weight by less than 44 grams.
4
Richard has 3 blue candles, 2 red candles and 6 green candles. The candles are identical apart from their colours. He arranges the 11 candles in a line.
4(a) [2]
Find the number of different arrangements of the 11 candles if there is a red candle at each end.
4(b) [4]
Find the number of different arrangements of the 11 candles if all the blue candles are together and the red candles are not together.
5
In Greenton, 70% of the adults own a car. A random sample of 8 adults from Greenton is chosen.
5(a) [3]
Find the probability that the number of adults in this sample who own a car is less than 6. A random sample of 120 adults from Greenton is now chosen.
5(b) [5]
Use an approximation to find the probability that more than 75 of them own a car.

Published by Cambridge Assessment International Education. Reproduced for study use.