CA Foundation · Quantitative Aptitude · Probability
Three urns hold balls as follows: Urn I has 2 white and 3 black, Urn II has 4 white and 1 black, Urn III has 3 white and 2 black. An urn is chosen at random and one ball is drawn, which is white. What is the probability that it came from Urn II?
The probability is 4/9. With equal priors of 1/3, the likelihoods of a white ball are 2/5, 4/5 and 3/5, summing to 9/5. Urn II's share is 4/5 divided by 9/5, which equals 4/9.
- A4/9Correct
- B1/3
- C4/5
- D3/9
Explanation
Each urn has prior 1/3. P(white) in the urns is 2/5, 4/5, 3/5. Total = (1/3)(9/5) = 3/5. P(Urn II | white) = (1/3)(4/5)/(3/5) = (4/15)/(9/15) = 4/9. Option 1/3 is the prior, and 4/5 is only the likelihood.
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