Question

A and B are two events such that $P\left(A\right)\ne 0$. Find$P\left(\frac{B}{A}\right)$if

A is a subset of B

$A\cap B=\varphi$

Answer 1

It is given that, $P\left(A\right)\ne 0$

Given A is a subset of B i.e $(A\cap B)$

$\Rightarrow A\cap B=A\Rightarrow P(A\cap B)=P\left(A\right)\therefore P\left(\frac{B}{A}\right)=\frac{P(B\cap A)}{P\left(A\right)}=\frac{P\left(A\right)}{P\left(A\right)}=1$

Here, $A\cap B=\varphi \Rightarrow P(A\cap B)=0\therefore P\left(\frac{B}{A}\right)=\frac{P(B\cap A)}{P\left(A\right)}=\frac{0}{P\left(A\right)}=0$