Question

Two dice are rolled one after the other.

The probability that the number on the first is smaller than the number on the second, is

• A. $\frac{1}{2}$
• B. $\frac{3}{4}$
• C. $\frac{7}{18}$
• D. $\frac{5}{12}$

Answer 1

The correct option is D

$\frac{5}{12}$

Explanation for the correct answer:

Two dice are thrown

The total number of outcomes in the sample space $n\left(S\right)$ are given as

$\Rightarrow$ $\mathrm{n}\left(\mathrm{S}\right)=6^2=36$

Let $\mathrm{A}$ be the event that the number on the first dice is smaller the number on the second dice

$\Rightarrow$ $\mathrm{A}=\left\{\left(1,2\right),\left(1,3\right),\left(1,4\right),\left(1,5\right),\left(1,6\right),\left(2,3\right),\left(2,4\right),\left(2,5\right)\left(2,6\right),\left(3,4\right),\left(3,5\right)\left(3,6\right)\left(4,5\right),\left(4,6\right)\left(5,6\right)\right\}$

$\Rightarrow$ $\mathrm{n}\left(\mathrm{A}\right)=15$

$\Rightarrow$ $\mathrm{p}\left(\mathrm{A}\right)=\frac{\mathrm{n}\left(\mathrm{A}\right)}{\mathrm{n}\left(\mathrm{S}\right)}$

$\Rightarrow$ $\mathrm{p}\left(\mathrm{A}\right)=\frac{15}{36}$

$\Rightarrow$ $\mathrm{p}\left(\mathrm{A}\right)=\frac{5}{12}$

Hence, the probability of getting the smaller number on the first dice when two dice are rolled is $\frac{5}{12}$.

Hence, option $\left(\mathrm{D}\right)$ is the correct answer.