Question

A sample space contains six sample points and events A, B, and C as shown in the Venn diagram. The probablities of the sample points are P(1)=0.15, P(2)=0.15, P(3)=0.15, P(4)=0.2, P(5)=0.15, P(6)=0.2.

Use the Venn diagram and the probabilities of the sample points to find:
P(B|C)
P(B¯¯¯¯|C¯¯¯¯)

Answer 1

(a) 0.65

(b) 3/7

(c) 6/13

Explanation:

(a) P(C') = 1 - p(5) -p(6) = 1 - 0.15 - 0.2

P(C') = 0.65

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(b) P(B|C) = P(BC)/P(C) = P(5)/(P(5)+P(6)) = 0.15/(0.15 +0.2)

P(B|C) = 3/7

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(c) P(B'|C') = P(B'C')/P(C') = (P(1) +P(2))/0.65 = (0.15+0.15)/0.65

P(B'|C') = 6/13