Question

What is the probability of rolling an even number of dots with a fair, six-sided die numbered one through six?

Short answer

The solution is$$\begin{gathered} P\left(\text{even}\right)=\frac{3}{6} \\ =\frac{1}{2} \\ =0.5 \end{gathered}$$

Step-by-step solution

Step : Given

We must determine the probability of rolling an even number of dots with a fair, six-sided die numbered one through six in the following question.

Concept used

Probability is a metric for determining how certain we are of the results of a certain experiment.

The probability is calculated using the following formula:

Probability $=\frac{\text{Farorable number of cases}}{\text{Total number of cases}}$

For example, if we flip a coin two times, the sample space associated with this random experiment is $\{HH,HT,TH,TT]$where T tails and H heads. Let's suppose A getting one tail. There are two outcomes which favors the event $\mathit{A}$

localid="1648043254326" $$\begin{gathered} \{HT,TH]\text{, so}P\left(A\right)=\frac{2}{4} \\ =0.5. \end{gathered}$$

Calculation

We know that while rolling a fair die, there are six possible results. The following are probable outcomes:

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

As a result, the favorable number of instances for rolling an even number is $32,4,6$, and the overall number of cases is $6$. As a result, using a fair, six-sided die, the chance of rolling an even number of dots is:

localid="1648029994258" $$\begin{gathered} P\left(\text{even}\right)=\frac{3}{6} \\ =\frac{1}{2} \\ =0.5 \end{gathered}$$