What is the Conditional Probability of Finding a Book in a Specific Box?

[Alexsandro]

Somebody could help me to find out the answer of the interesting question about conditional probability ?

"You are moving to other apartment and you need to find your probability book. It is inside of one box. There are n boxes to all. The probability of the book is inside of the box i is Pi and the probability of the book, being in the box i, to be found is Ai. Then what's the conditional probability of the book is in the box j, given that you it looked in box i and did not find. It analyzes the cases where i é igual ao j and i é diferente do j".

 

[lippyka]

For i = j:The conditional probability of the book being in box j, given that you looked in box i and did not find it, is Pj * (1 - Aj). For i ≠ j: The conditional probability of the book being in box j, given that you looked in box i and did not find it, is Pj.