Three identical Urns I, ll and III contain 4 white and 3 red balls, 3 white and 7 red balls and 2 white and 3 red balls respectively. An Urn is chosen at random and a ball is drawn out of it at random. If the ball is found to be white, what is the probability that Urn ll was selected?

Three identical Urns I, ll and III contain 4 white and 3 red balls, 3

1.	Three identical Urns I, ll and III contain 4 white and 3 red balls, 3 white and 7 red balls and 2 white and 3 red balls respectively. An Urn is chosen at random and a ball is drawn out of it at random. If the ball is found to be white, what is the probability that Urn ll was selected?
Answer» `P(U_1)=1/3` `P(U_2)=1/3` `P(U_3)=1/3` `P(W/U_1)=4/7` `P(W/U_2)=3/10` `P(W/U_3)=2/5` `P(U_2/W)=(P(U_2)P(W/U_2))/(P(U_1)P(W/U_1)+P(U_2)P(W/U_2)+P(U_3)P(W/U_3))` `=(1/33/10)/(1/34/7+1/33/10+1/32/5)` `=21/89`.

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Three identical Urns I, ll and III contain 4 white and 3 red balls, 3 white and 7 red balls and 2 white and 3 red balls respectively. An Urn is chosen at random and a ball is drawn out of it at random. If the ball is found to be white, what is the probability that Urn ll was selected?

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