Chapter 13.6, Problem 10PPS

To determine

The probability of less than $8$ is to be estimated in the form of fraction and percent

  

Answer to Problem 10PPS

The probability of less than $8$ in the form of fraction and percent are estimated as $\frac{7}{20}$

and $35\%$ 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: $n\left(S\right)$

Calculation:

Here, the numbers less than $8$ are:

  $1,2,3,4,5,6,7$

total $7$ numbers are there which are less than $8$ .

The probability of getting number less than $8$ in the fraction form is calculated as:

  $\begin{array}{l}P=\frac{n\left(E\right)}{n\left(S\right)}\\ P_8=\frac{7}{20}\end{array}$

In the percent form:

  $\begin{array}{l}P=\frac{n\left(E\right)}{n\left(S\right)}\times 100\\ P_8=\frac{7}{20}\times 100\\ P_8=35\%\end{array}$

Conclusion:

Hence, the probabilities are resulted as:

In the fraction form: $P_8=\frac{7}{20}$

In the percent form: $P_8=35\%$