Chapter 10, Problem 19CR

To determine

To find: The probability as a fraction and as a percent and describe the likelihood of the event as impossible, unlikely, equally likely, likely, or certain.

Answer to Problem 19CR

The probability in fraction is $\frac{3}{5}$ .

The probability in percent is $60\%$ .

Probability of the event is likely to occur.

Explanation of Solution

Given information: Ten sided solid whose identical faces are numbered with first ten square numbers.

Calculation: Ten sided solid whose identical faces are numbered with first ten square numbers.

The sample space is $\left\{1,4,9,16,25,36,49,64,81,100\right\}$ .

Total outcomes $=10$ .

Favourable outcomes is $\left\{16,25,36,49,64,81\right\}$ .

Number of favourable outcomes $=6$ .

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

  $\begin{array}{l}\mathrm{P}(2\mathrm{digit}\mathrm{number})=\frac{6}{10}=\frac{3}{5}\\ \mathrm{In}\mathrm{percent}=\frac{3}{5}\times 100\%=3\times 20\%=60\%\end{array}$

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

Thus, the probability in fraction is $\frac{3}{5}$ ,the probability in percent is $60\%$ and probability of the event is likely to occur.