Exercise 82 Let A B C D be a list of mutually independent ev

Exercise 8.2 Let A, B, C, D be a list of mutually independent events. Suppose

P (A ) = .3, P (B ) = .6, P (C ) = .4 and P (D ) = .8 .

Find the probabilities of the following events:

A B C D,

B D, B D,

and ((C –A )B ) D.

Solution

P(A B C D) = P(A)*P(B)*P(C\')*P(D) = 0.3*0.6*0.6*0.8=0.0864

P(B D) = P(B) +P(D)-P(B)*P(D) = 0.6+0.8-0.6*0.8 = 0.92

P(B\' D) = P(B\') +P(D)-P(B\')*P(D) = 0.4+0.8-0.4*0.8 = 0.88

P[((C –A )B ) D.] = P[(C –A )B )] +P(D) -P((C –A )B )*P(D) = P(C)*P(A\')*P(B) +P(D) -P(C)*P(A\')*P(B)*P(D) =0.4*0.7*0.6 +0.8 -0.4*0.7*0.6*0.8 = 0.8336