Probability Ques 98
The conditional probability that $X \geq 6$ given $X>3$ equals
(a) $\frac{125}{216}$
(b) $\frac{25}{216}$
(c) $\frac{5}{36}$
(d) $\frac{25}{36}$
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Answer:
Correct Answer: 98.(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} $
BETA
