Question

Bag A contains 2 red and 3 black balls while another bag B contains 3 red and 4 black balls. One ball is drawn at random from one of the bag and it is found to be red. Find the probability that it was drawn from bag B.

Answer 1

Probability of drawing a red ball from bag A = $\frac{2}{2+3}=\frac{2}{5}$

Probability of drawing a red ball from bag B = $\frac{3}{3+4}=\frac{3}{7}$

therefore probability that the drawn red ball belongs to bag B = $\frac{\frac{3}{7}}{\frac{2}{5}+\frac{3}{7}}$

$=\frac{3}{7}\times \frac{5\times 7}{14+15}$

$=\frac{15}{29}$