Question

Givin P(X)=0.35, P(Y)=0.45, and P(Y|X)=0.25, what are P(X and Y) and P(X or Y)

Answer 1

Answer:

$P(Y|X)=\frac{P(Y\cap X)}{P(Y)} \\ P(Y\cap X) = P(Y)P(Y|X) \\ = 0.45 \times 0.25 \\ \boxed{P(Y\cap X) =0.1125} \\ P(Y\cup X) = P(Y) + P( X) - P(Y\cap X) \\ = 0.45 + 0.35 - 0.1125 \\ \boxed{P(Y\cup X) =0.6875}$