Question

IF A and B are any two events such that P(A) + P(B) - P (A and B ) = P(A), then
(a) $P\left(\frac{B}{A}\right)=1$
(b) $P\left(\frac{A}{B}\right)=1$
(c) $P\left(\frac{B}{A}\right)=0$
(d) $P\left(\frac{A}{B}\right)=0$

Answer 1

Given, P(A)+ p(B) - P(A and B) = P(A)
$\Rightarrow P\left(A\right)+P\left(B\right)-P(A\cap B)=P\left(A\right)\Rightarrow P\left(B\right)-P(A\cap B)=0\Rightarrow P\left(B\right)=P(A\cap B)\Rightarrow 1=\frac{P(A\cap B)}{P\left(B\right)}\Rightarrow 1=P\left(\frac{A}{B}\right)[\because P(\frac{A}{B}=\frac{P(A\cap B)}{P\left(B\right)})]$