Question

A fair die is rolled repeatedly until a six is obtained. Let X denote the number of rolls required.

The probability that $X=3$ equals

• A. $\frac{25}{216}$
• B. $\frac{25}{36}$
• C. $\frac{5}{36}$
• D. $\frac{125}{216}$

Answer 1

The correct option is A $\frac{25}{216}$

Given: A fair die is rolled repeatedly until a six is obtained.

The probability of getting a $6$ in the third toss is

$P(X=3)$ $=(1-\frac{1}{6})(1-\frac{1}{6})\left(\frac{1}{6}\right)$
$=\frac{5\times 5\times 1}{6^3}$
$=\frac{25}{216}$