Chapter 10.6, Problem 24IP

To determine

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

Answer to Problem 24IP

The probability in fraction is $\frac{17}{20}$ .

The probability in percent is $85\%$ .

Probability of the event is likely 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 $\left\{1,2,3,7,8,9,10,11,12,13,14,15,16,17,18,19,20\right\}$ .

Number of favourable outcomes $=17$ .

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

  $\begin{array}{l}\mathrm{P}(\mathrm{not}4,5\mathrm{or}6)=\frac{17}{20}\\ \mathrm{In}\mathrm{percent}=\frac{17}{20}\times 100\%=17\times 5\%=85\%\end{array}$

Probability of event is more than $50\%$ , So the event is likely to occur.

Thus, the probability in fraction is $\frac{17}{20}$ ,the probability in percent is $85\%$ and probability of the event is likely to occur.