Question

If $A$ and $B$ are two independent events, then $P\left(\frac{A}{B}\right)=$

• A. $0$
• B. $1$
• C. $P\left(A\right)$
• D. $P\left(B\right)$

Answer 1

The correct option is C

$P\left(A\right)$

Explanation for the correct option:

Find the value of $P\left(\frac{A}{B}\right)$:

As we know, $\mathit{P}\left(\frac{A}{B}\right)\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{P}\mathbf{(}\mathbf{A}\mathbf{\cap }\mathbf{B}\mathbf{)}}{\mathbf{P}\mathbf{\left(}\mathbf{B}\mathbf{\right)}}$

$\because A$ and $B$ are independent events

Now, $P\left(\frac{\mathrm{A}}{\mathrm{B}}\right)=\frac{\mathrm{P}\left(\mathrm{A}\right).\mathrm{P}\left(\mathrm{B}\right)}{\mathrm{P}\left(\mathrm{B}\right)}$$\mathit{P}\mathbf{(}\mathit{A}\mathbf{\cap }\mathit{B}\mathbf{)}\mathbf{}\mathbf{=}\mathbf{}\mathit{P}\mathbf{\left(}\mathit{A}\mathbf{\right)}\mathbf{.}\mathit{P}\mathbf{\left(}\mathit{B}\mathbf{\right)}$

$\Rightarrow$ $\mathit{P}\mathbf{\left(}\frac{\mathbf{A}}{\mathbf{B}}\mathbf{\right)}\mathbf{}\mathbf{=}\mathbf{}\mathit{P}\mathbf{\left(}\mathit{A}\mathbf{\right)}$

Hence, Option ‘C’ is Correct.