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Two ums contain respectively 2 red, 3 wh...

Two ums contain respectively 2 red, 3 white and 3 red, 5 whiteb balls. One ball is drawn at random the first urn and transferred into the second. A ball is now drawn from the second urn and it turns out to be red Find the probabiliy that the transferred ball from first urn was white.

Text Solution

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`A-> 2R, 3W`
`B-> 3R, 5W`
Case- I: `P(R) = 2/5`
`P(R_B) = 4/9`
Case-II :`P(W_A) = 3/5`
`P(R_B)= 3/9 = 1/3`
`P(A_W/R) = (P(A_W)*P(B_R/A_W))/(P(A_W)*P(B_R/A_W) + P(A_R)P(B_R/A_R) `
`= (3/5 xx 1/3)/(3/5 xx 1/3 + 2/5 xx 4/9 )`
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