Chapter 10.1, Problem 17E

(a)

To determine

To find: the theoretical probability that the spinner stops on a multiple of 3

Answer to Problem 17E

The theoretical probability that the spinner stops on a multiple of 3 is: $0 .9$

Explanation of Solution

Given:

  

Calculation:

The outcomes for a specified event are called favorable outcomes. When all outcomes are equally likely, the theoretical probability is described as the ratio of number of favorable outcomes to total number of outcomes.

There are 10 sections in a spinner, and out of these, 9 sections have numbers which are multiplier than 3. Therefore, for the given problem, the probability of each outcome is as follows:

  $\begin{array}{l}P(\text{ multiplier of }3)=\frac{\text{ Number of favorable outcomes }}{\text{ Total number of outcomes }}\\ =\frac{9}{10}\\ =0.9\end{array}$

Therefore, the theoretical probability that the spinner stops on a multiple of 3 is: 0.9

Conclusion:

Therefore, the theoretical probability that the spinner stops on a multiple of 3 is: $0 .9$

(b)

To determine

To find: the experimental probability of stopping on a multiple of 3

Answer to Problem 17E

the experimental probability of stopping on a multiple of 3 is: $.67$

Explanation of Solution

Calculation:

The experimental probability is the ratio of number of successes to number of trials. In the given situation, the spinner is rotated 30 times and the spinner has stopped on multiple of three 20 times.

The experimental probability of spinner stopping on a multiple of 3 is as follows:

  $P($ multiplier of 3 $)=\frac{\text{ Number of successes }}{\text{ Number of trials }}$

  $\begin{array}{r}\hfill =\frac{20}{30}\\ \hfill =0.67\end{array}$

The experimental probability of stopping on a multiple of 3 is $.67$

Conclusion:

The experimental probability of stopping on a multiple of 3 is $.67$

(c)

To determine

To explain: why the probability found in part (b) is different frompart (a).

Answer to Problem 17E

The differences arises because, the probability in second part is based on number of trials, not possible outcomes.

Explanation of Solution

Calculation:

Experimental probability is purely based on experimental results, thus, the differences arises because, the probability in second part is based on number of trials, not possible outcomes.

Conclusion:

The differences arises because, the probability in second part is based on number of trials, not possible outcomes.