Question

Suppose that p(a) = .25 and p(bc) = .71, and p(a or
b.= .38. then the p(a|b) =

Answer 1

$P(B^C)=0.71\implies P(B)=1-0.71=0.29$

$P(A\cap B)=P(A)+P(B)-P(A\cup B)\implies P(A\cap B)=0.25+0.29-0.38=0.16$

$P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{0.16}{0.29}\approx0.55$