Question

A bag contains $5$ white balls, $3$ black balls, $4$ yellow balls. A ball is drawn from the bag, its colour is noted and put back into the bag with $5$ additional balls of the same colour. The process is repeated. The probability that a yellow ball is drawn in the $1^{s t}$ draw given that a white ball is drawn in the $2^{n d}$ draw is

• A. $\frac{9}{55}$
• B. $\frac{4}{17}$
• C. $\frac{1}{5}$
• D. $\frac{2}{11}$

Answer 1

Answer: (B)

$A=$ A yellow ball is drawn in the $1^{s t}$ draw
$B=$ A white ball is drawn in the $2^{n d}$ draw
$P\left(\frac{A}{B}\right)=\frac{P \left(A \cap B\right)}{P \left(B\right)}=\frac{\frac{4}{12} \times \frac{5}{17}}{\frac{5}{12} \times \frac{10}{17} + \frac{3}{12} \times \frac{5}{17} + \frac{4}{12} \times \frac{5}{17}}$
$=\frac{4}{17}$