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JEE Advance - Mathematics (2011 - Paper 1 Offline - No. 13)

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 at random from $${U_1}$$ and put into $${U_2}$$. Now $$1$$ ball is drawn at random from $${U_2}$$ being white is
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 at random from $${U_1}$$ and put into $${U_2}$$. Now $$1$$ ball is drawn at random from $${U_2}$$ being white is
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 at random from $${U_1}$$ and put into $${U_2}$$. Now $$1$$ ball is drawn at random from $${U_2}$$ being white is
Given that the drawn ball from $${U_2}$$ is white, the probability that head appeared on the coin is
$${{17} \over {23}}$$
$${{11} \over {23}}$$
$${{15} \over {23}}$$
$${{12} \over {23}}$$

Explanation

$$P\left( {{H \over W}} \right) = {{P(W/H) \times P(H)} \over {P(W/T)\,.\,P(T) + (W/H)\,.\,P(H)}}$$

$$ = {{{1 \over 2}\left( {{3 \over 5} \times 1 + {2 \over 5} \times {1 \over 2}} \right)} \over {23/30}} = {{12} \over {23}}$$

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