Question

Let P(E) denote the probability of an event E. Given $P\left(A\right)=1,P\left(B\right)=\frac{1}{2}$, the values of P(A/B) and P(B/A) respectively are

• A. $\frac{1}{4},\frac{1}{2}$
• B. $\frac{1}{2},\frac{1}{4}$
• C. $\frac{1}{2},1$
• D. $1,\frac{1}{2}$

Answer 1

The correct option is D $1,\frac{1}{2}$

Given that P(A) = 1
$\Rightarrow$ A is sure event
$\Rightarrow$ A will definitely occur
So A is independent from B

$\mathrm{Hence},P(A\cap B)=P\left(A\right).P\left(B\right)=1\times \frac{1}{2}=\frac{1}{2}$

$\mathrm{So},\begin{array}{c}P\left(\frac{A}{B}\right)=\frac{P(A\cap B)}{P\left(B\right)}=1,\\ P\left(\frac{B}{A}\right)=\frac{P(B\cap A)}{P\left(A\right)}=\frac{1}{2}\end{array}\}$