Box A contains 2 black and 3 red balls while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box, then the probability that it has come from box B is

Question

Question

This question was previously asked in

BPSC Asstt. Prof. ME Held on Nov 2015 (Advt. 22/2014)

Answer 1

Concept:

Let A be the event of choosing box A, and B be the event of choosing box B, and R is the event of drawing a red ball.

Baye's theorem:

where

P(A) = Probability of event A.

P(B) = Probability of event B.

= Probability of event R when event B already occur

= Probability of event R when event A already occur

= Probability of event B when event R already occur

Calculation:

Given:

Box A

Box B

2 Black

3 Red

3 Black

4 Red

P(A) = 2P(B), ,

Now, the probability of drawing a ball from box B, provided it is a red ball