Question

A box contains $4$ white and $3$ black balls. Two balls are drawn successively and is found that second ball is white, then the probability that Ist ball is also white is

• A. $\frac{5}{16}$
• B. $\frac{1}{2}$
• C. $\frac{1}{5}$
• D. $\frac{1}{3}$

Answer 1

Answer: (B)

$A =2$ nd ball in white
$B_1=1$ st ball in white
$B_2=1$ st is black
$P\left(B_1 / A\right)=\frac{p\left(A / B_1\right) p\left(B_1\right)}{p\left(A / B_1\right) p\left(B_1\right)+p\left(A / B_2\right) p\left(B_2\right)}$
$=\frac{\frac{4}{7} \times \frac{3}{6}}{\frac{4}{1} \times \frac{3}{6}+\frac{3}{7} \times \frac{4}{6}}$