Determine all joint probabilities listed below from the foll

Determine all joint probabilities listed below from the following information:

P(A)=0.77,

P(A\')=0.23,

P(B|A)=0.53,

P(B|A\')=0.72

P(A and B) =

P(A and B\') =

P(A\' and B) =

P(A\' and B\')

Solution

Before starting to find the required let us find these

P(A/B) = P(AB)/P(B) and P(B/A) = P(AB)/P(A)

Hence 0.53 = P(AB)/P(A)

P(A/B\') = P(AB\')/P(B\')

P(A and B) =

P(AB) = 0.53(0.77)

=0.4081

P(A and B\') = P(AB\')

= P(A)-P(AB)

=0.77-0.4081

= 0.3619

P(A\' and B) = P(A\')P(B/A\')

= 0.23(0.72)=0.1656

P(A\' and B\') = P(A\') P(B\'/A\')

= 0.23(0.77-0.72)

= 0.115