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A ball is in any one of n boxes and is in the ith box with
Chapter 3, Problem 4TE(choose chapter or problem)
Problem 4TE
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 αi. Show that the conditional probability that the ball is in box j, given that a search of box i did not uncover it, is
Questions & Answers
QUESTION:
Problem 4TE
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 αi. Show that the conditional probability that the ball is in box j, given that a search of box i did not uncover it, is
ANSWER:
Step 1 of 2
Our goal is
We need to show that the conditional probability that the ball is in box j, given that a search of box i did not uncover.
Let and
be the two events.
The ball represents in the box i is and
The search of box j yields a success or “finds” the ball.
Then the statement of the problem is
P( ) =
