Probability Ques 101
Passage IV
There are $n$ urns each containing $(n+1)$ balls such that the ith urn contains ‘i’white balls and $(n+1-i)$ red balls. Let $u _i$ be the event of selecting ith urn, $i=1,2,3, \ldots, n$ and $W$ denotes the event of getting a white balls.
$(2006,5\ M)$
If $n$ is even and $E$ denotes the event of choosing an even numbered urn $[P\left(u_i\right)=\frac{1}{n}]$, then the value of $P(W \mid E)$ is
(a) $\frac{n+2}{2 n+1}$
(b) $\frac{n+2}{2(n+1)}$
(c) $\frac{n}{n+1}$
(d) $\frac{1}{n+1}$
Show Answer
Answer:
Correct Answer: 101.(b)
Solution:
Formula:
$P (\frac{W}{E})=\frac{2+4+6+\ldots}{\frac{n(n+1)}{2}}=\frac{n+1}{2(n+1)}$
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