Question

A computer randomly generates an integer from 1 to 10. Find the probability of the given event. Write your answer as a percent.

$P\left(\text{factor}\text{of}\text{20}\right)$

Short answer

The probability of getting factor of 20 is 50%.

Step-by-step solution

Step 1. Given Information.

A computer generates an integer from 1 to 10.

Step 2. Formula used.

Probability:

$\text{P}=\frac{\text{favorable} \text{outcomes}}{\text{total} \text{outcomes}}$

Step 3. Find the probability of getting factor of 20.

To calculate the probability of getting factor of 20, there are 10 total outcomes. It is needed to calculate favorable outcomes.

$\begin{array}{c}\text{favourable\hspace{0.17em}\hspace{0.33em}out\hspace{0.17em}comes}=\left\{1,2,4,5,10\right\}\\ =5\end{array}$

Therefore, the probability of getting factor of 20 is obtained as,

$\begin{array}{c}\text{P}\left(\text{of\hspace{0.17em}gettingfactorof20}\right)=\frac{\text{favorable\hspace{0.17em}\hspace{0.33em}outcome}}{\text{total\hspace{0.17em}\hspace{0.33em}outcome}}\\ \text{P}\left(\text{of\hspace{0.17em}gettingfactorof20}\right)=\frac{5}{10}\\ =\frac{1}{2}\end{array}$

Therefore, the probability of getting $\text{factor of 20}$ is $\frac{1}{2}$.

Step 4. Convert the obtained fraction form into percent.

Multiply $\frac{1}{2}$ by 100% to convert the fraction form in percent.

$\begin{array}{c}\text{P}\left(\text{of\hspace{0.17em}gettingfactorof20}\right)=\frac{1}{2}\times 100\%\\ \text{P}\left(\text{of\hspace{0.17em}gettingfactorof20}\right)=50\%\end{array}$

Step 5. Conclusion.

The probability of getting $\text{factor of 20}$ is 50%.