Probability 4 Question 13
13. The conditional probability that $X \geq 6$ given $X>3$ equals
(a) $\frac{125}{216}$
(b) $\frac{25}{216}$
(c) $\frac{5}{36}$
(d) $\frac{25}{36}$
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)
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Answer:
Correct Answer: 13. (d)
Solution:
- $P{(X \geq 6) /(X>3)}=\frac{P{(X>3) /(X \geq 6)} \cdot P(X \geq 6)}{P(X>3)}$
$$ =\frac{1 \cdot \frac{5}{6}^{5} \cdot \frac{1}{6}+\frac{5}{6}^{6} \cdot \frac{1}{6}+\ldots \infty}{\frac{5}{6}^{3} \cdot \frac{1}{6}+\frac{5}{6}^{4} \cdot \frac{1}{6}+\ldots \infty}=\frac{25}{36} $$
