Find the probabilities of the following events

Question

events A and B of a sample space S, but assume that Pr[A′] = 0.4, Pr[B] = 0.55, and Pr[A′∩ B] = 0.2.

Find the probabilities of the following events:

(1) Pr[A∩B] =

(2) Pr[A∪B] =

(1) Pr[A′∪B]

Answer 1

Pr(A')=.4, Pr(A)=.6

Pr(B)=.55, Pr(B')=.45

Pr(A'∩B)=Pr(B-A)=.2, Pr(A∪B')=.8

 

Pr(B)=Pr(B-A)+Pr(A∩B)

   .55=  .2      + Pr(A∩B)

 

Pr(A∩B)=.35

 

Pr(A∪B)=Pr(A)+Pr(B)-Pr(A∩B)

Pr(A∪B)=    .6 + .55  -.35 = .8

 

Pr(B∪A')=Pr(A')+Pr(B)-Pr(BA')

Pr(B∪A')=   .4   + .55 - .2=.75

 

And, if you want it,

Pr(A∪B')=Pr(B')+Pr(A)-Pr(A∩B')
.8 =.45 + .6-Pr(A∩B')

Pr(A∩B')=.25