Determine all joint probabilities listed below from the foll

Determine all joint probabilities listed below from the following information:

P(A)=0.79,P(Ac)=0.21,P(B|A)=0.41,P(B|Ac)=0.77

P(A and B) =

P(A and B^c) =

P(Ac and B) =

P(Ac and B^c)=

Solution

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

Thus P(A and B) = P(B|A) * P(A) = 0.41 * 0.79 = 0.3239

P ( Ac and B ) = P(B|Ac) * P(Ac) = 0.77 * 0.21 = 0.1617

B^c = ??