Question

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

Short answer

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

Step-by-step solution

Given

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

Concept used

Probabilityisametricfordetermininghowcertainweareoftheresultsofacertainexperiment.

Theprobabilityiscalculatedusingthefollowingformula:

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

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 A

localid="1648043311671" $$\begin{gathered} [HT,TH\},\text{so}P\left(A\right)=\frac{2}{4} \\ =0.5\text{.} \end{gathered}$$

Calculation

We know that while rolling a fair die, there are six possible results. The following are the probable outcomes: $\{1,2,3,4,5,6\}$

As a result, the favorable number of instances for rolling a prime number is $3\{2,3,5\}$, and the overall number of cases is $6$.

As a result, $P(primenumber)=\frac{3}{6}=\frac{1}{2}=0.5$is the probability of rolling a prime number of dots with a fair, six-sided die.