Answer to Question #219007 in Statistics and Probability for batho

Question

a document is equally likely to be in any of the 3 box files.a seach of ith the box will discover the document with probability pi. what is the probability that, the document is in the 1st box given that i have searched the first box twice and not found it

Answer 1

Solution:

There are 3 boxes.

The probability that document will be in any of them$=\dfrac13$

Given, a search of i^th box will discover the document with probability pi.

So, a search of 1^st box will discover the document with probability = p(1)=p.

Now, the probability that, the document is in the 1st box given that I have searched the first box twice and not found it=P(the document is in the 1st box and I have searched the first box twice and not found it)/P(I have searched the first box twice and not found it)

$=\dfrac{\dfrac13}{(1-p)(1-p)}=\dfrac{1}{3(1-p)^2}$