Chapter 10.7, Problem 5IP

a.

To determine

To find: The experimental probability of the spinner landing on $4$ .

Answer to Problem 5IP

The experimental probability of the spinner landing on $4$ is $\frac{3}{10}$ .

Explanation of Solution

Given Information: Spinner was spun $20$ times and table containing relevant data.

Calculation:

  $\begin{array}{l}P(4)=\frac{\text{Number of times spinner landed on 4}}{\text{Number of times spinner was spun}}\\ \\ =\frac{6}{20}\\ \\ =\frac{3}{10}\text{or about 30\%}\end{array}$

Thus, the experimental probability of the spinner landing on $4$ is $\frac{3}{10}$ .

b.

To determine

To find: The experimental probability of the spinner landing on $3$ .

Answer to Problem 5IP

The experimental probability of the spinner landing on $3$ is $\frac{1}{4}$ .

Explanation of Solution

Given Information: Spinner was spun $20$ times and table containing relevant data.

Calculation:

  $\begin{array}{l}P(3)=\frac{\text{Number of times spinner landed on 3}}{\text{Number of times spinner was spun}}\\ \\ =\frac{5}{20}\\ \\ =\frac{1}{4}\text{or 25\%}.\end{array}$

Thus, the experimental probability of the spinner landing on $3$ is $\frac{1}{4}$ .

c.

To determine

To find: The theoretical probability of the spinner landing on $3$ and then to compare it to the experimental probability.

Answer to Problem 5IP

Theoretical probability for $3$ is same as experimental probability.

Explanation of Solution

Given Information: Spinner was spun $20$ times and table containing relevant data. Experimental probability of $3$ from previous part.

Calculation:

Theoretical probability:

  $\begin{array}{l}P(3)=\frac{\text{Number of times 3 is printed on spinner}}{\text{Total segments in spinner}}\\ \\ =\frac{1}{4}\end{array}$

Thus, theoretical probability for $3$ is same as experimental probability.