a The sections of the given spinner have the same areas.
We will find the theoretical probability that the spinner stops on a multiple of 3. Recall how to calculate theoretical probability.
Theoretical Probability = Number of Favorable Outcomes/Total Number of Outcomes
The favorable outcomes for this exercise are the sections whose numbers are a multiple of 3, and all possible outcomes are all sections of the spinner. Now we can identify the number of the favorable outcomes and the total number of outcomes.
Outcomes
Number of Outcomes
Favorable Outcomes
6, 9, 12, 15, 18, 21, 24, 27, and 30
9
All Possible Outcomes
4, 6, 9, 12, 15, 18, 21, 24, 27, and 30
10
Now we will write the theoretical probability of stopping on a multiple of 3.
P(stopping on a multiple of3) &= 9/10
&=90 %
The probability is 910, or 90 %.
b Now we have spun the spinner 30 times. The spinner stops on a multiple of 3 twenty times. Now we will find the experimental probability of stopping on a multiple of 3. Let's recall how to calculate it.
Experimental Probability = Number of Successes/Number of Trials
Since we spin the spinner 30 times, our number of trials is 30. Besides this, since the favorable outcome occurs 20 times, our number of successes is 20. We can write the experimental probability with this information.
c We will explain why the probability that we found in Part B is different from the probability that we found in Part A. To do so let's review the formulas for theoretical probability and experimental probability.
Theoretical Probability
Number of favorable outcomes/Total number of outcomes
Experimental Probability
Number of successes/Number of trials
We can see that the experimental probability is based on trials, whereas the theoretical probability is based on possible outcomes.
