Question

Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black. Select the correct answer from above options

Answer 1

P(R)=3/7,P(R)=4/7 P(A/R)=5/10=1/2 P(A/B)=4/10=2/5 `P(B/A)=(P(B)*P(A/B))/(P(R)*P(A/R)+P(B)*P(A/B)` `P(B/A)=((4/7)(2/5))/((4/7)(2/5)+(3/7)(1/2))` `P(B/A)=16/31`