Question

A and B are two events such that P (A) ≠ 0. Find P (B|A), if (i) A is a subset of B (ii) A ∩ B = Φ

Answer 1

Use the formula for conditional probability,

$P(B|A)=\frac{P(BA)}{P(A)}$.

Given $P(A) \neq 0$.

i) When $A\subset B$, we have $BA=B \cap A=A$.

So,

$P(B|A)=\frac{P(BA)}{P(A)}=\frac{P(A)}{P(A)}=1$.

ii) When $BA=B \cap A=\phi$,

$P(B|A)=\frac{P(BA)}{P(A)}=\frac{P(\phi)}{P(A)}=\frac{0}{P(A)}=0$