Question

A six faced fair dice is thrown until $1$ comes. The probability that $1$ comes in even no. of trails is

• A. $\frac{5}{11}$
• B. $\frac{5}{6}$
• C. $\frac{6}{11}$
• D. $\frac{1}{6}$

Answer 1

The correct option is A $\frac{5}{11}$

Probability of getting $1$ in nay particular trail $=\frac{1}{6}$
$\therefore$ The probability of getting $1$ in even number of trails $=$ probability of getting $1$ in $I{I}^{nd}$ trail $+$ probability of getting $1$ in $I{V}^{th}$ trail $+...$
$=\frac{5}{6}\times \frac{1}{6}+\frac{5}{6}\times \frac{5}{6}\times \frac{5}{6}\times \frac{1}{6}+...$
$=\frac{\frac{5}{6}\times \frac{1}{6}}{1-{\left(\frac{5}{6}\right)}^2}=\frac{5}{11}$