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Question

Let U1 and U2 be two urns such that U1 contains 3 white and 2 red balls and U2 contains only 1 white ball. A fair coin is tossed. If the head appears then 1 ball is drawn at random from U1and put into U2. However, if the tail appears then 2 balls are drawn at random from U1 and put into U2. Now, 1 ball is drawn at random from U2. Given that the drawn ball from U2 is white, the probability that a head appeared on the coin is


A

1723

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B

1123

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C

1523

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D

1223

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Solution

The correct option is D

1223


Explanation for Correct Answer:

Given: Urn U1contains 3 white and 2 red balls .

U1=2+3=5

Urn U2 contains only 1 white ball

U2=1

Let W be the event of drawing white ball.

Then, the probability of drawing white balls from U2, when head appears on coin.

P1=12×35×22+25×12=12×35×1+15=12×3+15=12×45=25

Now, the probability of drawing white balls from U2, when tail appears on coin.

P2=12×35×22+25×12+2512×310×1+110×13+610×23=12×35+15+2512×9+1+1230=12×45+2512×2230=12×45+151115=25+1175=2330

Now, to find the probability that head appeared on the coin,

P=P1P2=252330=25×3023=1223

Therefore, the probability that head appeared on the coin is 1223

Hence, option (D) is the correct answer


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