Chapter 0.5, Problem 1E

(a)

To determine

To add a column showing the experimental probability of landing on each given color with the next spin.

Explanation of Solution

Given Information:

The following is the table showing the results of various spins

Color	Frequency
Red
Blue
Yellow	$9$
Orange	$12$
Purple	$5$
Green	$11$
Total	$50$

The total number of spins is $50$ .

The probability for any event $A$ is given by $P\left(A\right)=\frac{\text{favorable}\text{}\text{}\text{cases}}{\text{total}\text{cases}}$

For the red color favorable cases are $6$ and the total cases are $50$ , therefore, the probability is given by $P\left(A\right)=\frac{6}{50}$ which is equal to $0.12$ .

Make the table again by calculating the probabilities as shown.

Color	Frequency	Probability
Red		$\frac{6}{50}=0.12$
Blue		$\frac{7}{50}=0.14$
Yellow	$9$	$\frac{9}{50}=0.18$
Orange	$12$	$\frac{12}{50}=0.24$
Purple	$5$	$\frac{5}{50}=0.10$
Green	$11$	$\frac{11}{50}=0.22$
Total	$50$

The table shows the probabilities for different color spinners.

(b)

To determine

Draw the bar diagram showing the experimental probabilities.

Explanation of Solution

GRAPH:

The following bar graph shows the experimental probabilities.

Take color on x - axis and probability on y - axis and draw the bar graph as shown below.

  

Bar graph for the experimental probabilities.

(c)

To determine

Draw a table by adding a column that showing the theoretical probability of the spinner.

Explanation of Solution

There are six colors and all colors have equal probabilities.

Since, the total probability is $1$ and there are $6$ colors, Therefore, probability of each color will be $0.16$ .

The following table shows the theoretical probabilities in the table.

Color	Frequency	Probability
Red		$0.16$
Blue		$0.16$
Yellow	$9$	$0.16$
Orange	$12$	$0.16$
Purple	$5$	$0.16$
Green	$11$	$0.16$
Total	$50$

The table showing the theoretical probabilities.

(d)

To determine

Create a bar diagram showing the theoretical probabilities.

Explanation of Solution

GRAPH:

To plot the bar graph, proceed as follows.

Take color on x - axis and probability on y - axis and draw the bar graph as shown below.

  

Bar graph for the theoretical probabilities.

(e)

To determine

Interpret the graph by comparing the graphs created in above parts (b) and (d)

Explanation of Solution

In the first bar graph the experimental probabilities are given which is maximum for orange. Therefore, the probability of spinner landing on orange is more than green. So according the bar graph higher the length of bar, higher the probability of landing on that color.

But in the second bar graph all the bars have equal length implying that probability of landing on all the colors is same. All the colors have equal probability.