A ball is in any one of n boxes and is in the ith box with probability Pi If the ball is in box i, a search of that box will uncover it with probability i Show that the conditional probability that the ball is in box j, given that a search of box i did not uncover it, is , if i i if j i...

Let N i denote the event that the ball is n ...

A ball is in any one of n boxes and is in the ith box with probability

Question:

A ball is in any one of n boxes and is in the ith box with probability Pi. If the ball is in box i, a search of that box will uncover it with probability Î±i. Show that the conditional probability that the ball is in box j, given that a search of box i did not uncover it, is