Question

Two fair dice are rolled.

Determine the probability that the sum of the two dice is 7.

Short answer

The probability is$\frac{1}{6}$

Step-by-step solution

Step 1. Given Information

The given statement is the sum of the two dice is 7.

Step 2. Calculation

The probability of an event is given by the number of ways the event can occur divided by the total number of outcomes in the sample space.

When two dice are rolled sample space is given by $n\left(S\right)=36$that is total number of elements in the sample space.

Let E represent the event 'the sum of two dice is 6' that is$n\left(E\right)=6$

On substituting the values in the formula, we get,

$$\begin{gathered} P=\frac{n\left(E\right)}{n\left(S\right)} \\ =\frac{6}{36} \\ =\frac{1}{6} \end{gathered}$$