Chapter 10.7, Problem 6IP

a.

To determine

To find: The experimental probability of spinning a sum of $6$ .

Answer to Problem 6IP

The experimental probability for spinning a sum of $6$ is $\frac{3}{10}$ .

Explanation of Solution

Given Information: Spinners were each spun $50$ times and table containing relevant data.

Calculation:

  $\begin{array}{l}P(6)=\frac{\text{Number of times sum was 6}}{\text{Number of times spinner was spun}}\\ =\frac{15}{50}\\ =\frac{3}{10}\end{array}$

Thus, the experimental probability for spinning a sum of $6$ is $\frac{3}{10}$ .

b.

To determine

To find: The experimental probability of spinning a sum of $8$ .

Answer to Problem 6IP

The experimental probability for spinning a sum of $8$ is $\frac{4}{25}$ .

Explanation of Solution

Given Information: Spinners were each spun $50$ times and table containing relevant data.

Calculation:

  $\begin{array}{l}P(8)=\frac{\text{Number of times sum was 8}}{\text{Number of times spinner was spun}}\\ =\frac{8}{50}\\ =\frac{4}{25}\text{or 16\%}\end{array}$

Thus, the experimental probability for spinning a sum of $8$ is $\frac{4}{25}$ .

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 6IP

Theoretical probability is less than the experimental probability.

Explanation of Solution

Given Information: Spinners were each spun $50$ times and table containing relevant data. Experimental probability of spinning a sum of $8$ from previous part.

Calculation:

The possible outcomes of the experiment are:

  $\begin{array}{llll}(1,1)\hfill & (1,2)\hfill & (1,3)\hfill & (1,4)\hfill \\ (2,1)\hfill & (2,2)\hfill & (2,3)\hfill & (2,4)\hfill \\ (3,1)\hfill & (3,2)\hfill & (3,3)\hfill & (3,4)\hfill \\ (4,1)\hfill & (4,2)\hfill & (4,3)\hfill & (4,4)\hfill \end{array}$

Theoretically, out of total $4\times 4=16$ cases, in only one case ( $(4,4)$ , i.e., when both the spinners return $4$ ) , the sum turns out to be $8$ .

  $\begin{array}{l}P(8)=\frac{\text{Number of outcomes in which sum is 8}}{\text{Total number of outcomes}}\\ =\frac{1}{16}\text{ or 6}\text{.25\%}\end{array}$

As $\frac{4}{25}>\frac{1}{16}$, so the sum of $8$ turned out to be more than expected.

Thus, theoretical probability is less than the experimental probability.