Question

A pair of fair dice is tossed repeatedly until a sum of four or an odd sum appears. Then the probability that a sum of four appear first is

• A. $\frac{1}{3}$
• B. $\frac{2}{5}$
• C. $\frac{3}{8}$
• D. $\frac{1}{7}$

Answer 1

The correct option is D $\frac{1}{7}$

A pair of fair dice is tossed repeatedly therefore probability of
$P$(sum of four)$=\frac{3}{36}=\frac{1}{12},$
$P$(odd sum )$=\frac{18}{36}=\frac{1}{2}$
$P$(neither sum of four nor odd sum )$=1-\frac{1}{12}-\frac{1}{2}=\frac{5}{12}$
Required probability$P=\frac{1}{12}+\frac{5}{12}\times \frac{1}{12}+{\left(\frac{5}{12}\right)}^2\frac{1}{12}+....$
$P=\frac{\frac{1}{12}}{1-\frac{5}{12}}=\frac{1}{7}$