Question

Construct a copy of figure 3.14 in your text, where the first outcome is one of A and B the second outcome in each case is one of a and b. Use the following probabilities instead of those given in your text:

Pr[A]=13
Pr[B]=23
Pr[a|A]=57
Pr[b|A]=27
Pr[a|B]=23
Pr[b|B]=13
Find the following missing probabilities:

(1) Pr[B]=

(2) Pr[b]=

(3) Pr[b|B]=

(4) Pr[B|b]=

Can someone please explain to me how to apply Bayes's theory to this problem?