Question

Bag I contains 3 red and 4 black balls while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag II.

Answer 1

A= taking red ball
B=selecting a Ball
`P(B_1)=P(B_2)=1/2`
`P(A/B_1)=3/7` and `P(A/B_2)=5/11`
`P(B_2/A)=(P(A/B_2)P(B_2))/(P(A/B_2)P(B_2)+P(A/B_1)P(B_1))`
`P(B_2/A)=((5/11)(1/2))/((5/11)(1/2)+(3/7)(1/2))`
=`35/68`.