Question

Bag A contains 5 white and 4 black balls, and bag B contains 7 white and 6 black balls. One ball is drawn from the bag A and without noticing its colour, is put in the bag B. If a ball is then drawn from bag B, find the probability that it is black in colour.

Answer 1

Case 1: When a white ball is transferred from the bag A to bag B

\(P_1=\frac{5}{5+4}=\frac{5}{9}\)

Now, bag B contains 8 white and 6 black balls. Then, the probability of drawing a black ball from bag B is P₂ = 6/14

 

∴ The probability of both the events occuring together

\(=P_1P_2=\frac{5}{9}\times\frac{6}{14}=\frac{30}{126}=\frac{5}{21}\)

Case 2: When a black ball is transferred from the bag A to bag B

\(P_3=\frac{4}{5+4}=\frac{4}{9}\)

Now, bag B contains 7 white and 7 black balls. Then, the probability of drawing a black ball from bag B is P₄ = 7/14

∴ The probability of both the events occuring together

\(=P_3P_4=\frac{4}{9}\times\frac{7}{14}=\frac{2}{9}\)

∴ The required probability

\(=P_1P_2+P_3P_4=\frac{5}{21}+\frac{2}{9}=\frac{15+14}{63}=\frac{29}{63}\)