E1 - Selection of Bag A

E2 - Selection of Bag B

E3 - Selection of Bag C

A - red ball is selected

since Bag A is chosen when , 1 turns up when a fair die is rolled

P(E1) - 1/6,

since Bag B is chosen when ,2 0r 3 turns up when a fair die is rolled

P(E2) - 2/6

and since Bag C is chosen when 4 or 5 or 6 occurs when a fair die is rolled

P(E3) - 3/6

Bag A contains 3 red and 2 white balls - P(A/E1) =3/5 Bag Bcontains 3 red and 5white balls - P(A/E2)=3/7 Bag C contains 4 red and 5 white balls-P(A/E3)=4/9

Formula:- P(E2/A)= P(E2).P(A/E2)/ P(E2).P(A/E2)+P(E1).P(A/E1)+P(E3).P(A/E3)

substitute

P(E2/A)=(2/6.3/7)/2/6.3/7+1/6.3/5+3/6.4/9

=90/293 .