Given Pr[E]=0.44 and Pr(E U F)=0.78, determine Pr[F]

Question

a.IF E & F are disjoint events.

 

Have determined that this one is .34

 

 

b. If E & F are independent events.

Answer 1

Assuming P(E ? F) = P(E U F)

 

     P(E U F) = P(E) + P(F) - P(E∩F)

 

If E and F are disjoint, then P(E∩F) = 0.  Hence:

 

     P(E U F) = P(E) + P(F)

     0.78 = 0.44 + P(F)

     0.34 = P(F)