Chapter 10.6, Problem 15IP

To determine

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

Answer to Problem 15IP

The probability in fraction is $\frac{2}{5}$ .

The probability in percent is $40\%$ .

Probability of the event is unlikely 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 $=\left\{2,3,5,7,11,13,17,19\right\}$ .

Number of favourable outcomes $=8$ .

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

  $\begin{array}{l}\mathrm{P}(\mathrm{prime}\mathrm{number})=\frac{8}{20}=\frac{2}{5}\\ \mathrm{In}\mathrm{percent}=\frac{2}{5}\times 100\%=2\times 20\%=40\%\end{array}$

Probability of event is less than $50\%$ , So the event is unlikely to occur.

Thus, the probability in fraction is $\frac{2}{5}$ ,the probability in percent is $40\%$ and probability of the event is unlikely to occur.