Question

What is the probability of getting a multiple of $3$ when a die is tossed?

Answer 1

Step 1: Calculate the total number of outcomes

When we roll a die, we obtain the following results:

$\left\{1,2,3,4,5,6\right\}$

For that, the total number of outcomes $=n\left(S\right)=6$

Step 2: Calculate the favorable outcomes

Let $R$ be the event of getting a multiple of 3.

$R=\left\{3,6\right\}$

Number of favorable outcomes of the event $R=n\left(R\right)=2$

Step 3:Calculate the probability

Formula of probability: $P\left(R\right)=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes}$

Then the probability is $P\left(R\right)=\frac{n\left(R\right)}{n\left(S\right)}=\frac{2}{6}=\frac{1}{3}$.

Hence, the probability of getting a multiple of $3$ when a die is thrown is $\frac{1}{3}$.