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Question

A bag A contains 4 green and 3 red balls and bag B contains 4 red and 3 green balls. One bag is taken at random and a ball is drawn and noted to be green. The probability that it comes from bag B is


A

27

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B

23

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C

37

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D

13

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Solution

The correct option is C

37


Explanation for correct option:

Step-1: Finding probability using classical approach.

Given, bag 'A' contains 4 Green and 3 red balls and bag B contains 4 red and 3 green balls.

Let EG be the event in which the green ball is selecting, EAbe the event in which the ball selecting from bag A, Ebbe the event in which the ball selecting from bag B.

Probability of ball drawn from the bag A, PA=12

Probability of ball drawn from the bag B, PB=12

Probability of green ball drawn from the bag A, PGA=47

Probability of green ball drawn from the bag B, PGB=37

Step-2: Applying Bayes theorem,

Probability of green ball drawn from bag B,

PBG=PGBPBPGAPA+PGBPB=37×1247×12+37×12=3144+314=37

Therefore, the probability that the green ball comes from the bag Bis 37

Hence, correct answer is option C


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