Chapter 12.7, Problem 1CYU

a.

To determine

To find the experimental probability of having a winner in the second group.

Answer to Problem 1CYU

The $\text{Experimental probability of having a winner in the second group}=\frac{3}{10}\text{ or 30}\%$ .

Explanation of Solution

Given information:

The given statement is:

“Games at the fair require the majority of players to lose in order for game owners to make a profit. New games are tested to make sure they have sufficient difficulty. The results of three test groups are listed in the table. The owners want a maximum of $33\%$ players to win. There were $50$ participants in each test group.”

  

Formula used:

The following formula is used:

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

Calculation:

The experimental probability that the participant was a winner in the second group can be calculated by:

  $\begin{array}{l}\text{Experimental probability of having a winner in the second group}=\frac{15}{50}\\ \text{Experimental probability of having a winner in the second group}=\frac{3}{10}\text{ or 30}\%\end{array}$

Hence, the $\text{Experimental probability of having a winner in the second group}=\frac{3}{10}\text{ or 30}\%$ .

b.

To determine

To find the experimental probability of winning for all the three groups.

Answer to Problem 1CYU

The $\text{Experimental probability of winning for all 3 groups}=\frac{47}{150}\text{ or 31}\%$ .

Explanation of Solution

Given information:

The given statement is:

“Games at the fair require the majority of players to lose in order for game owners to make a profit. New games are tested to make sure they have sufficient difficulty. The results of three test groups are listed in the table. The owners want a maximum of $33\%$ players to win. There were $50$ participants in each test group.”

  

Formula used:

The following formula is used:

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

Calculation:

The experimental probability of winning for all the three groups can be calculated by:

  $\begin{array}{l}\text{Experimental probability of winning for all 3 groups}=\frac{13+15+19}{50+50+50}\\ \text{Experimental probability of winning for all 3 groups}=\frac{47}{150}\text{ or 31}\%\end{array}$

Hence, the $\text{Experimental probability of winning for all 3 groups}=\frac{47}{150}\text{ or 31}\%$ .