Let event A1 : The ball is drawn from 1st box
and
event A2 : The ball is drawn from the 2nd box.
∴ P(A ) = 1/2, P(A2) = 1/2
Let event B: The ball drawn is pink.
There are 5 balls in the 1st box, of which 3 are pink.
∴ P(B/A1) = 3/5
There are 9 balls in the 2nd box, of which 5 are pink.
∴ P(B/A2) = 5/9
(i) By Bayes’ theorem, the probability that a pink ball is drawn from the first box, is given by
(ii) By Bayes’ theorem, the probability that a pink ball is drawn from the second box, is given by