Chapter 12.7, Problem 9PPS

a.

To determine

To find the probability of rolling a $\text{2}$ .

Answer to Problem 9PPS

  $\text{The probability of rolling a 2}=\frac{4}{25}\text{ or 16\%}$

Explanation of Solution

Given information:

The results recorded after rolling a die $\text{25}$ time is given in the table below:

  

Formula used:

The following formula is used:

  $\text{Experimental probability}=\frac{\text{Frequency of an outcome}}{\text{Total number of trials}}$

Calculation:

The probability of rolling a $\text{2}$ can be calculated by:

  $\text{The probability of rolling a 2}=\frac{4}{25}\text{ or 16\%}$

b.

To determine

To find the probability of rolling a prime number.

Answer to Problem 9PPS

The probability of rolling a prime number is $\frac{14}{25}\text{ or 56\%}$ .

Explanation of Solution

Given information:

The results recorded after rolling a die $\text{25}$ time is given in the table below:

  

Formula used:

The following formula is used:

  $\text{Experimental probability}=\frac{\text{Frequency of an outcome}}{\text{Total number of trials}}$

Calculation:

The probability of rolling a prime number is $\frac{14}{25}\text{ or 56\%}$ .

c.

To determine

To find the probability of rolling an even number or $\text{3}$ .

Answer to Problem 9PPS

  $\text{The probability of rolling an even number or 3}=\frac{17}{25}\text{ or 68\%}$

Explanation of Solution

Given information:

The results recorded after rolling a die $\text{25}$ time is given in the table below:

  

Formula used:

The following formula is used:

  $\text{Experimental probability}=\frac{\text{Frequency of an outcome}}{\text{Total number of trials}}$

Calculation:

The probability of rolling aneven number or $\text{3}$ can be calculated by:

  $\text{The probability of rolling an even number or 3}=\frac{17}{25}\text{ or 68\%}$

d.

To determine

To compare the experimental probabilities to the theoretical probabilities.

Answer to Problem 9PPS

The experimental probability and the theoretical probability are comparatively similar.

Explanation of Solution

Given information:

The results recorded after rolling a die $\text{25}$ time is given in the table below:

  

  $\text{The probability of rolling a 2}=\frac{4}{25}\text{ or 16\%}$

The probability of rolling a prime number is $\frac{14}{25}\text{ or 56\%}$ .

  $\text{The probability of rolling an even number or 3}=\frac{17}{25}\text{ or 68\%}$

Formula used:

The following formula is used:

  $\text{Experimental probability}=\frac{\text{Frequency of an outcome}}{\text{Total number of trials}}$

Calculation:

The theoretical probability can be calculated by:

  $\begin{array}{l}\text{The theoretical probability of rolling a 2}=\frac{1}{6}\text{ or 16}\text{.67\%}\\ \text{The theoretical probability of rolling a prime number}=\frac{3}{6}\text{ or 50\%}\\ \text{The theoretical probability of rolling an even number or 3}=\frac{4}{6}=66.67\%\end{array}$

Hence, the experimental probability and the theoretical probability are comparatively similar.