Question

Two dices are thrown simultaneously. The probability of obtaining a total score of $5$ is

• A. $\frac{1}{9}$
• B. $\frac{1}{18}$
• C. $\frac{1}{12}$
• D. $\frac{1}{36}$

Answer 1

Answer: (A)

$\frac{1}{9}$

Two dices are thrown simultaneously.

$\therefore S=\left\{\right(1,1\left)\right(1,2\left)\right(1,3\left)\right(1,4\left)\right(1,5\left)\right(1,6\left)\right(2,1\left)\right(2,2\left)\right(2,3\left)\right(2,4\left)\right(2,5\left)\right(2,6\left)\right(3,1\left)\right(3,2\left)\right(3,3\left)\right(3,4\left)\right(3,5\left)\right(3,6\left)\right(4,1\left)\right(4,2\left)\right(4,3\left)\right(4,4\left)\right(4,5\left)\right(4,6\left)\right(5,1\left)\right(5,2\left)\right(5,3\left)\right(5,4\left)\right(5,5\left)\right(5,6\left)\right(6,1\left)\right(6,2\left)\right(6,3\left)\right(6,4\left)\right(6,5\left)\right(6,6\left)\right\}$

$\Rightarrow n\left(S\right)=36$

Let $A$ be the event of obtaining a total score of $5$.

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

$\therefore n\left(A\right)=4$.

Probability of obtaining a total score of $5$ is $P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{4}{36}=\frac{1}{9}$.