Question

If $4P\left(A\right)=6P\left(B\right)=10P(A\cap B)=1$, then $P\left(\frac{B}{A}\right)$

• A. $\frac{2}{5}$
• B. $\frac{3}{5}$
• C. $\frac{7}{10}$
• D. $\frac{19}{60}$

Answer 1

The correct option is A

$\frac{2}{5}$

Explanation for correct option:

Given that

$\begin{array}{rcl}4P\left(A\right)& =& 6P\left(B\right)=10P(A\cap B)=1\end{array}$

$\begin{array}{rcl}P\left(\frac{B}{A}\right)& =& \frac{P(A\cap B)}{P\left(A\right)}\\ & \Rightarrow & P\left(\frac{B}{A}\right)=\frac{{\displaystyle \frac{1}{10}}}{{\displaystyle \frac{1}{4}}}\\ P\left(\frac{B}{A}\right)& =& \frac{4}{10}\\ & \mathbf{=}& \frac{\mathbf{2}}{\mathbf{5}}\end{array}$

Hence, option (A) is correct.