Question

A fair die is tossed repeatedly until a six is obtained. Let $X$ denote the number of tosses 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

$\frac{25}{216}$

Explanation for correct option:

Step 1: Define possible outcomes:

Possible outcomes $=\left\{1,2,3,4,5,6\right\}$

Number of tosses required until six is obtained $=X$

Step 2: Find the required probability:

The probability of a fair die does not obtain six $=\frac{5}{6}$

$\therefore$Probability for the first two tosses $=\frac{5}{6}$

Probability of getting six in the third toss $=\frac{1}{6}$

$\begin{array}{rcl}\therefore \mathrm{P}\left(\mathrm{X}=3\right)& =& \left(\frac{5}{6}\right)\left(\frac{5}{6}\right)\left(\frac{1}{6}\right)\\ & =& \frac{25}{216}\end{array}$

Hence, Option(A) is the correct answer.