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Let {U}_{{1}} and {U}_{{2}} be two urns such that {U}_{{1}} co

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

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Let

U_{1}

and

U_{2}

be two urns such that

U_{1}

contains 3 white and 2 red balls, and

U_{2}

contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from

U_{1}

and put into

U_{2}

. However, if tail appears then 2 balls are drawn from

U_{1}

and put into

U_{2}

. Now, 1 ball is drawn at random from

U_{2}

Given that the drawn ball from

U_{2}

is white, the probability that head appeared on the coin is

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Question Text

Let

U_{1}

and

U_{2}

be two urns such that

U_{1}

contains 3 white and 2 red balls, and

U_{2}

contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from

U_{1}

and put into

U_{2}

. However, if tail appears then 2 balls are drawn from

U_{1}

and put into

U_{2}

. Now, 1 ball is drawn at random from

U_{2}

Given that the drawn ball from

U_{2}

is white, the probability that head appeared on the coin is

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