Question 384295
P(A|Y) = P(AY)/P(Y) = (P(Y|A)*P(A))/(P(Y|A)*P(A)) + P(Y|B)*P(B)) = 
{{{(7/13)*0.58/((7/13)*0.58 + (3/8)*0.42) = 0.6648}}}.  This is by direct use of Bayes' Theorem.