A sample space contains six sample points and events A B and

A sample space contains six sample points and events A, B, and C as shown in the Venn diagram. The probabilities of the sample points are P(1) =0.2, P(2) = 0.35, P(3) =0.25, P(4) = 0.05, P(5) = 0.05, P(6) = 0.1. Use the Venn diagram and the probabilities of the sample points to find:

Solution

a)

P(B\') = 1 - P(B) = 1 - [P(3) + P(4) + P(5)]

= 1 - [0.25+0.05+0.05]

= 0.65 [answer]

***************

b)

P(A|B) = P(3) / [P(B)] = 0.25/0.35

= 0.714285714 [answer]

*************

c)

A and C are mutually exclusive.

Hence,

P(C\'|A) = 1 [answer]