Chapter 10.6, Problem 32IP

a.

To determine

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

Answer to Problem 32IP

The probability in fraction is $\frac{1}{3}$ .

The probability in percent is $33.33\%$ .

Probability of the event is unlikely to occur.

Explanation of Solution

Given information: A bag contains $3$ red tiles, $5$ black tiles and $4$ white tiles is given.

Calculation: A bag contains $3$ red tiles, $5$ black tiles and $4$ white tiles is given.

Total outcomes $=12$ .

Number of favourable outcomes $=4$ .

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

  $\begin{array}{l}\mathrm{P}(\mathrm{white}\mathrm{tiles})=\frac{4}{12}=\frac{1}{3}\\ \mathrm{In}\mathrm{percent}=\frac{1}{3}\times 100\%=\frac{100}{3}\%=33.33\%\end{array}$

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

Thus, the probability in fraction is $\frac{1}{3}$ ,the probability in percent is $33.33\%$ and probability of the event is unlikely to occur.

b.

To determine

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

Answer to Problem 32IP

The probability in fraction is $\frac{2}{3}$ .

The probability in percent is $66.66\%$ .

Probability of the event is likely to occur.

Explanation of Solution

Given information: A bag contains $3$ red tiles, $5$ black tiles and $4$ white tiles is given.

Calculation: A bag contains $3$ red tiles, $5$ black tiles and $4$ white tiles is given.

Total outcomes $=12$ .

Number of favourable outcomes $=4$ .

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

  $\begin{array}{l}\mathrm{P}(\mathrm{not}\mathrm{white}\mathrm{tiles})=\frac{3+5}{12}=\frac{8}{12}=\frac{2}{3}\\ \mathrm{In}\mathrm{percent}=\frac{2}{3}\times 100\%=\frac{200}{3}\%=66.66\%\end{array}$

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

Thus, the probability in fraction is $\frac{2}{3}$ ,the probability in percent is $66.66\%$ and probability of the event is likely to occur.