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Learn/ A Level Mathematics/ Past Papers/ 2020/ Oct/Nov 2020 /Paper 5 (Variant 1)

Probability & Statistics 1 — Variant 1

A Level Mathematics · 9709/51 · Oct/Nov 2020

Question Paper

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Mark Scheme

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Questions

4 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
Two ordinary fair dice, one red and the other blue, are thrown. Event AA is ‘the score on the red die is divisible by 3’. Event BB is ‘the sum of the two scores is at least 9’.
1(a) [2]
Find P(A∩B)P(A \cap B).
1(b) [2]
Hence determine whether or not the events AA and BB are independent.
3
Kayla is competing in a throwing event. A throw is counted as a success if the distance achieved is greater than 3030 metres. The probability that Kayla will achieve a success on any throw is 0.250.25.
3(a) [2]
Find the probability that Kayla takes more than 66 throws to achieve a success.
3(b) [3]
Find the probability that, for a random sample of 1010 throws, Kayla achieves at least 33 successes.
4
The random variable XX takes each of the values 1,2,3,41, 2, 3, 4 with probability 14\frac{1}{4}. Two independent values of XX are chosen at random. If the two values of XX are the same, the random variable YY takes that value. Otherwise, the value of YY is the larger value of XX minus the smaller value of XX.
4(a) [4]
Draw up the probability distribution table for YY.
4(b) [2]
Find the probability that Y=2Y = 2 given that YY is even.
5
The time in hours that Davin plays on his games machine each day is normally distributed with mean 3.53.5 and standard deviation 0.90.9.
5(a) [3]
Find the probability that on a randomly chosen day Davin plays on his games machine for more than 4.24.2 hours.
5(b) [3]
On 90%90\% of days Davin plays on his games machine for more than tt hours. Find the value of tt.
5(c) [3]
Calculate an estimate for the number of days in a year (365365 days) on which Davin plays on his games machine for between 2.82.8 and 4.24.2 hours.

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