Question

there are 10 boxes each of them having 7 red and 6 white balls. having chosen two random boxes one ball is drawn simultaneously from each box and transferred to the other box. now a box is again selected from the 10 boxes and a ball is chosen from it.the probability of this ball being white is:

Answer 1

P (Box2 selected/White) = P (White/Box2selected) P(Box2selected)/P(White)

P(Box2selected/White) = P(White/Box2selected) P(Box2selected) P(White/Box1selected) P(Box1selected) + P(White/Box2selected) P(Box2selected)+  P(White/Box3selected) P(Box3selected)

Substituting the values, we get

P (Box2 selected/White) = 2/3

Similarly,

P (Box3 selected/White) = 1/3

P (other ball is White) = P (other ball is White/Box2 selected) P(Box2 selected/White) + P (other ball is White/Box3 selected) P(Box3 selected/White)