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Q.

Bag A contains 3 white, 2 red balls. Bag B contains 1 white ball. A fair coin is tossed. If head appears one ball is transferred from A to B. If tail appears then 2 balls are transferred from A to B. Now one ball is drawn from B, the chance that it is white is $λ$ then $30 λ$ is___

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answer is 23.

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Detailed Solution

A contains $3 W, 2 R$
B contains 1w
P(getting white)
$= p (E_{1}) p (\frac{W}{E_{1}}) + p (E_{2}) p (\frac{W}{E_{2}})$
$= \frac{1}{2} [\frac{3}{5} \times \frac{2}{2} + \frac{2}{5} \times \frac{1}{2}] + \frac{1}{2} [\frac{^{3} C_{2}}{^{5} C_{2}} . \frac{^{3} C_{2}}{^{3} C_{2}} + \frac{^{2} C_{2}}{^{5} C_{2}} \frac{^{1} C_{1}}{^{3} C_{1}} + \frac{^{3} C_{1} \times^{2} C_{1}}{^{5} C_{2}} . \frac{^{2} C_{1}}{^{3} C_{1}}]$
$= \frac{23}{30}$

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