StudentAidProbability & Statistics 1 — Variant 1
A Level Mathematics · 9709/51 · May/June 2022
Questions
3 of 6 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
1(a)
[2]
Find the number of different arrangements of the 8 letters in the word DECEIVED in which all three Es are together and the two Ds are together.
1(b)
[4]
Find the number of different arrangements of the 8 letters in the word DECEIVED in which the three Es are not all together.
2
There are men and women in a Book Club. The committee of the club consists of five of its members. Mr Lan and Mrs Lan are members of the club.
2(a)
[2]
In how many different ways can the committee be selected if exactly one of Mr Lan and Mrs Lan must be on the committee?
2(b)
[4]
In how many different ways can the committee be selected if Mrs Lan must be on the committee and there must be more women than men on the committee?
6
Janice is playing a computer game. She has to complete level and level to finish the game. She is allowed at most two attempts at any level. For level , the probability that Janice completes it at the first attempt is . If she fails at her first attempt, the probability that she completes it at the second attempt is . If Janice completes level , she immediately moves on to level . For level , the probability that Janice completes it at the first attempt is . If she fails at her first attempt, the probability that she completes it at the second attempt is .
6(a)
[1]
Show that the probability that Janice moves on to level is .
6(b)
[3]
Find the probability that Janice finishes the game.
6(c)
[4]
Find the probability that Janice fails exactly one attempt, given that she finishes the game.
Published by Cambridge Assessment International Education. Reproduced for study use.