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Three identical Urns I, ll and III conta...

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?

Text Solution

Verified by Experts

`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))`
`=(1/3*3/10)/(1/3*4/7+1/3*3/10+1/3*2/5)`
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