Question

If 4 P(A) =6 P(B) = 10 P$\left(A\cap B\right)$ = 1, then P(B/A) = ______________.

Answer 1

For any two events A and B, given 4 P(A) = 6 P(B) = 10 P$\left(A\cap B\right)$ = 1
i.e $P\left(A\right)=\frac{1}{4},P\left(B\right)=\frac{1}{6},P\left(A\cap B\right)=\frac{1}{10}$
$\begin{array}{rcl}\therefore P\left(\frac{B}{A}\right)& =& \frac{P\left(A\cap B\right)}{P\left(A\right)}\\ & =& \frac{{\displaystyle \frac{1}{10}}}{{\displaystyle \frac{1}{4}}}\\ & =& \frac{1}{10}\times 4\\ P\left(\frac{B}{A}\right)& =& \frac{2}{5}\end{array}$