SATHEE: Probability 4 Question 13

Probability 4 Question 13

13. The conditional probability that $X \geq 6$ given $X > 3$ equals

(a) $\frac{125}{216}$

(b) $\frac{25}{216}$

(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, $i = 1, 2, 3, \dots, n$ and $W$ denotes the event of getting a white balls.

$(2006, 5$ M)

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Answer:

Correct Answer: 13. (d)

Solution:

$P (X \geq 6) / (X > 3) = \frac{P (X > 3) / (X \geq 6) \cdot P (X \geq 6)}{P (X > 3)}$

$= \frac{1 \cdot {\frac{5}{6}}^{5} \cdot \frac{1}{6} + {\frac{5}{6}}^{6} \cdot \frac{1}{6} + \dots \infty}{{\frac{5}{6}}^{3} \cdot \frac{1}{6} + {\frac{5}{6}}^{4} \cdot \frac{1}{6} + \dots \infty} = \frac{25}{36}$

Passage IV

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Probability 4 Question 13

13. The conditional probability that X≥6 given X>3 equals

Passage IV

Answer:

Passage IV

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13. The conditional probability that $X \geq 6$ given $X > 3$ equals