Chapter 13.6, Problem 12PPS

To determine

The probability of getting not prime numbers is to be estimated in the form of fraction and percent

  

Answer to Problem 12PPS

The probability of getting not prime numbers in the form of fraction and percent are estimated as $\frac{3}{5}$ and $60\%$ respectively.

Explanation of Solution

Given:

  $n\left(S\right)=20$

Concept Used:

Probability of an event is calculated as:

  $P=\frac{n\left(E\right)}{n\left(S\right)}$

Where,

The probability of an event: $P$

The number of favourable outcomes: $n\left(E\right)$

The total number of events in the sample space: $n\left(S\right)$

Prime number is the number which has only two factors such as first is itself and the second factor is $10$

Calculation:

Out of $20$ numbers, there are $12$ not prime numbers such as $1,4,6,8,9,10,12,14,15,16,18,20$

So, $n\left(E\right)=12$

The probability of getting not prime number in the fraction form is calculated as:

  $\begin{array}{l}P=\frac{n\left(E\right)}{n\left(S\right)}\\ P_{Np}=\frac{12}{20}\\ P_{Np}=\frac{3}{5}\end{array}$

In the percent form:

  $\begin{array}{l}P=\frac{n\left(E\right)}{n\left(S\right)}\times 100\\ P_{Np}=\frac{3}{5}\times 100\\ P_{Np}=60\%\end{array}$

Conclusion:

Hence, the probabilities are resulted as:

In the fraction form: $P_{Np}=\frac{3}{5}$

In the percent form: $P_{Np}=60\%$