Question

If two fair dice are rolled, what is the probability that the sum of the dice is at most $5$?

• A. $\frac{5}{36}$
• B. $\frac{6}{36}$
• C. $\frac{10}{36}$
• D. $\frac{26}{36}$

Answer 1

Answer: (C)

$\frac{10}{36}$

When two dice are rolled then,

The total number of outcomes=$6^2=36$

The favorable outcomes that the sum of the dice is at most $5=\left\{\right(1,1),(1,2),(1,3),(1.4),(2,1),(2,2),(2,3),(3,1),(3,2),(4,1\left)\right\}$

$\therefore$ Number of favorable outcomes $=10$

$\therefore$ Required probability=$\frac{10}{36}$