Chapter 13.6, Problem 11PPS

To determine

The probability of odd numbers is to be estimated in the form of fraction and percent

  

Answer to Problem 11PPS

The probability of getting odd numbers in the form of fraction and percent are estimated as $\frac{1}{2}$ and $50\%$ 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:

Out of $20$ numbers, there are $10$ odd numbers are $1,3,5,7,9,11,13,15,17,19$

So, $n\left(E\right)=10$

The probability of getting odd number in the fraction form is calculated as:

  $\begin{array}{l}P=\frac{n\left(E\right)}{n\left(S\right)}\\ P_O=\frac{10}{20}\\ P_O=\frac{1}{2}\end{array}$

In the percent form:

  $\begin{array}{l}P=\frac{n\left(E\right)}{n\left(S\right)}\times 100\\ P_O=\frac{1}{2}\times 100\\ P_O=50\%\end{array}$

Conclusion:

Hence, the probabilities are resulted as:

In the fraction form: $P_O=\frac{1}{2}$

In the percent form: $P_O=50\%$