Question

What is the probability of getting a sum of $5$ or $6$ when a pair of dice is thrown once?

Answer 1

Step 1: Find the number of favorable outcomes:

The sample space obtained when throwing a pair of dice will be,

$$\begin{gathered} \text{n(S)=}{\left(\text{possible outcomes of throwing a dice}\right)}^{\text{number of dices thrown}} \\ \text{n(S)=}{\left(6\right)}^2 \\ \text{n(S)=36} \end{gathered}$$

Thus, the number of possible outcomes will be $36$

Also, the favorable outcomes of getting a sum of $5\text{or}6$ is $(1,4),(2,3),(3,2),(4,1),(1,5),(2,4),(3,3),(4,2),(5,1)$.

Thus, the number of favorable outcomes will be $9$

Step 2: Use the formula for probability:

$\text{Probability=}\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

Thus, the probability will be,

$$\begin{gathered} \text{Probability=}\frac{9}{36} \\ \text{=}\frac{1}{4} \end{gathered}$$

Hence, probability of getting a sum of $5$ or $6$ when a pair of dice is thrown will be $\frac{1}{4}$.