Paragraph: A fair die is tossed repeatedly until a six is obtained. Let $X$ denotes the number of tosses required. Question: The conditional probability that $X \geq 6$ given $X3$ equals

Question

Paragraph: A fair die is tossed repeatedly until a six is obtained. Let $X$ denotes the number of tosses required. Question: The conditional probability that $X \geq 6$ given $X>3$ equals

Aicharya · Accepted Answer

$P((X \geq 6) /(X>3))$ $ \begin{aligned} & =\frac{P((X>3) /(X \geq 6)) \cdot P(X \geq 6)}{P(X>3)} \ & =\frac{1 \cdot\left[\left(\frac{5}{6}ight)^5 \cdot \frac{1}{6}+\left(\frac{5}{6}ight)^6 \cdot \frac{1}{6}+\ldots \inftyight]}{\left[\left(\frac{5}{6}ight)^3 \cdot \frac{1}{6}+\left(\frac{5}{6}ight)^4 \cdot \frac{1}{6}+\ldots \inftyight]}=\frac{25}{36} \ & \end{aligned} $

Paragraph: A fair die is tossed repeatedly until a six is obtained. Let $X$ denotes the number of tosses…

Solution