A sample space S has three events A B and C The events A and

A sample space S has three events, A, B, and C. The events A and C are disjoint, and the events A and B are independent. In addition, it is the case that:

Pr[A]= .5

Pr[B]= .3

Pr[C]= .2

Pr[B n C]= .05

Question: Pr[A\' n B n C\'] = ?

Solution

Pr[A\' n B n C\'] = P(B)-P(A n B)-P(B n C) = 0.3 - 0.5*0.3 - 0.05 = 0.1