Chapter 10.6, Problem 18IP

To determine

To find: The probability as a fraction and as a percent.

Answer to Problem 18IP

The probability in fraction is $1$ .

The probability in percent is $100\%$ .

Probability of the event is certain to occur.

Explanation of Solution

Given information: A dartboard is given in figure is divided into $20$ equal sections.

Calculation: A dartboard is given in figure is divided into $20$ equal sections.

The sample space is $\left\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20\right\}$ .

Total outcomes $=20$ .

Favourable outcomes $\left\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20\right\}$ .

Number of favourable outcomes $=20$ .

  $\mathrm{P}(\mathrm{event})=\frac{\mathrm{number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{number}\mathrm{of}\mathrm{total}\mathrm{outcomes}}$

  $\begin{array}{l}\mathrm{P}(\mathrm{less}\mathrm{than}21)=\frac{20}{20}=1\\ \mathrm{In}\mathrm{percent}=1\times 100\%=100\%\end{array}$

Probability of event is equal to $100\%$ , So the event is certain to occur.

Thus, the probability in fraction is $1$ ,the probability in percent is $100\%$ and probability of the event is certain to occur.