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)=0.2,
P(3)=0.3,
P(4)=0.05,
P(5)=0.05,
P(6)=0.25.

Use the Venn diagram and the probabilities of the sample points to find:
(a) P(C)
(b) P(C|B)
(c) P(Ā|B)

Answer 1

(a) 0.65 (b) 3/7 (c) 6/13Step-by-step explanation:(a) P(C') = 1 - p(5) -p(6) = 1 - 0.15 - 0.2 P(C') = 0.65__(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__(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