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4 Unit A2 2: Applied Mathematics (A-level only)

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Question 200

Three car clubs are called Vintage (VVV), Supercar (SSS) and Classic (CCC).

No member belongs to both the Vintage club and the Classic club. Some members belong to both the Vintage club and the Supercar club, and some belong to both the Supercar club and the Classic club. No member belongs to all three clubs.

For a car owner chosen at random from a large town, the probabilities of the separate regions are

P(V∩S′)=0.24P(V \cap S') = 0.24P(V∩S′)=0.24, P(V∩S)=0.16P(V \cap S) = 0.16P(V∩S)=0.16, P(S∩V′∩C′)=0.12P(S \cap V' \cap C') = 0.12P(S∩V′∩C′)=0.12, P(S∩C)=aP(S \cap C) = aP(S∩C)=a, P(C∩S′)=0.15P(C \cap S') = 0.15P(C∩S′)=0.15, and the probability of belonging to none of the three clubs is bbb

a.

Explain why P(V∩C)=0P(V \cap C) = 0P(V∩C)=0.

[1]
b.

Given that V V\,V and S S\,S are independent, find the value of aaa.

[3]
c.

Find the value of bbb.

[2]
d.

Find P(V∣S′)P(V \mid S')P(V∣S′).

[2]
Markscheme

4 Unit A2 2: Applied Mathematics (A-level only) Questions

  1. A Level
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