Chapter 7.1, Problem 33E

To determine

To find: The probability of getting prime number in percent when a computer generates random integers from $1\text{to}\text{10}$ in percent.

Answer to Problem 33E

The probability of getting prime number is $50\%$ .

Explanation of Solution

Given information: A computer generates an integer from $1\text{to}\text{10}$ .

Calculation:

To calculate the probability of getting prime number, it is needed to calculate the total outcome and favourable outcome

  $\begin{array}{l}\text{total}\text{}\text{outcomes}=\left\{1,2,3,4,5,6,7,8,9,10\right\}=\text{10}\\ \text{favourable}\text{}\text{out}\text{comes}=\left\{2,3,5,7,9\right\}=5\end{array}$

Therefore, the probability of getting prime number is obtained as,

  $\begin{array}{l}\text{P(of}\text{getting}\text{prime}\text{number)=}\frac{\text{favorable}\text{outcome}}{\text{total}\text{outcome}}\\ \text{P(of}\text{getting}\text{prime}\text{number})=\frac{5}{10}\\ \text{To}\text{convert}\text{fraction}\text{form}\text{in}\text{percent}\text{multiply}\text{by}\text{100\%}\\ \text{P(of}\text{getting prime}\text{number)}=\frac{1}{2}\times 100\%\\ \text{P(of}\text{getting}\text{prime}\text{number)}=50\%\end{array}$

Hence, The probability of getting prime number is $50\%$ .