A bag contains 3 red and 4 black balls and another bag has 4 red and 2 black balls. One bag is selected at random and from the selected bag a ball is drawn. Let `A` be the event that the first bag is selected, `B` be the event that the second bag is selected and `C` be the event that the ball drawn is red. Find `P(A)`, `P(C//A)` and `P(C//B)`.

Explanation

A bag contains 3 red and 4 black balls and another bag has 4 red and 2 black balls.
`text (P(first bag is selected))=P(A)=1/2`
`C` be the event that the ball drawn is red.
`P(CnnA) ->`red ball is selected from bag `A`.
`P(CnnA)=1/2xx3/7`
`=3/14`
so,`P(C/A)=(P(CnnA))/(P(A))=(3/14)/(1/2)`
`=3/7`
`P(CnnB) ->`red ball is selected from bag `B`.
`P(CnnB)=1/2xx4/6`
`=1/3`
so,`P(C/B)=(P(CnnB))/(P(B))=(1/3)/(1/2)`
`=2/3`