Question

Given P(X) = 0.5, P(Y) = 0.4, and P(Y|X) = 0.3, what are P(X and Y) and P(X or Y)?

Answer 1

Use the definition of conditional probability to find the "and" probability:

$P(Y\mid X)=\dfrac{P(X\cap Y)}{P(X)}\implies P(X\cap Y)=0.3\times0.5=0.15$

Use the inclusion/exclusion principle to find the "or" probability:

$P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)=0.5+0.4-0.15=0.75$