Question

If $P\left(A\right)=0.6,P\left(B\right)=0.7$ and $P(A\cup B)=0.9$, then find $P\left(\frac{A}{B}\right)$ and $P\left(\frac{B}{A}\right)$.

Answer 1

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$⟹0.9=0.7+0.6-P(A\cap B)⟹P(A\cap B)=0.4$

$P\left(\frac{A}{B}\right)=\frac{P(A\cap B)}{P\left(B\right)}$

$⟹P\left(\frac{A}{B}\right)=\frac{0.4}{0.7}=\frac{4}{7}$

$P\left(\frac{B}{A}\right)=\frac{P(A\cap B)}{P\left(A\right)}=\frac{0.4}{0.6}=\frac{2}{3}$