IIT-JEE 2011 · Paper 1 · Mathematics Q61

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MathematicsSingle correct+3 / -1Question 61 of 69

Passage

Paragraph for Question Nos. 61 and 62

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 $U_2$ .

The probability of the drawn ball from $U_2$ being white is

\dfrac{13}{30}

\dfrac{23}{30}

\dfrac{19}{30}

\dfrac{11}{30}

Answer and worked solution

Official answer: B

Head (½): one ball moves; U₂ then has 2 balls. $P(W)=\frac35\cdot1+\frac25\cdot\frac12=\frac45$ .

Tail (½): two balls move; U₂ has 3 balls with on average $1+2\cdot\frac35=\frac{11}5$ white, so $P(W)=\frac{11}{15}$ .

Total. $\frac12\left(\frac45+\frac{11}{15}\right)=\frac{23}{30}$ .

(B)

Topics:Conditional probability Classical probability

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IIT-JEE 2011 · Paper 1, Mathematics question 61