Q7 of 12 Page 13

There are two bags A and B. Bag A contains 3 white and 4 red balls whereas bag B contains 4 white and 3 red balls. Three balls are drawn at random (without replacement) from one of the bags and are found to be two white and one red. Find the probability that these were drawn from bag B.[CBSE 2016]

Given: Bag A contains 3 white and 4 red balls while Bag B contains 4 white and 3 red balls


Let E1 = Selecting bag A, E2 = selecting bag B


Probability of selecting the bag is given by



Now the probability of the balls drawn from bag A


Total number of ways of getting 2 white and 1 red ball from bag A = 3C24C1 = 12


Total possible outcome is = 7C3 = 35


So


Now the probability of the balls drawn from bag B


Total number of ways of getting 2 white and 1 red ball from bag B = 4C23C1 = 18


So,


Probability of the balls being drawn from bag B is given by


Formula: Bayes theorem



Hence, probability that these were drawn from bag B

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