Let C1 C2 C3 be independent events with probabilities 12 13

Let C1, C2, C3 be independent events with probabilities 1/2, 1/3, 1/4, respectively.

a) Compute P(C1 U C2 U C3)

As they are independent events, then the probability of their intersections is just the product of the probabilities of the events.

P(C1 U C2 U C3) = P(C1) + P(C2) + P(C3) - P(C1 n C2) - P(C2 n C3) - P(C1 n C3) + P(C1 n C2 n C3)

= (1/2) + (1/3) + (1/4) - (1/2)*(1/3) - (1/3)*(1/4) - (1/3)*(1/5) + (1/3)*(1/4)*(1/5)

= 3/4 [ANSWER]

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

P(C1\' n C2\'|C3 U C2) = P(C1\' n C2\' n (C3 U C2)) / P(C3 U C2)

= P(C1\') P(C2\') P(C3 U C2) / P(C3 U C2)

= P(C1\') P(C2\')

= (1-1/2)(1-1/3)

= 1/3 [ANSWER]