- #1

CAF123

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## Homework Statement

Consider 3 urns. Urn A contains 2 white and 4 red balls, Urn B contains 8 white and 4 red balls and Urn C contains 1 white and 3 red balls. If 1 ball is selected from each urn, what is the probability that the ball chosen from urn A was white given that exactly 2 white balls were selected?

## The Attempt at a Solution

Let E be the event that a white ball was chosen from urn A

Let F be the event that exactly 2 white balls were selected.

Given that the same colour of balls are indistinguishable , we have |s| = (2 choose 1) x (2 choose 1) x (2 choose 1) = 8 possibilities

Therefore F = {(WRW),(WWR),(RWW)} and E = {(WWW),(WRW),(WWR),(WRR)}

So, [tex] P(E|F) = \frac{P(EF)}{P(F)} = \frac{\frac{2}{8}}{\frac{3}{8}} = 2/3 [/tex]

The given answer is 7/11, which is slightly below this - where is the error?

Many thanks.