Jamison has a fair spinner with 8 equally sized sections labeled 1 through 8. He conducts an experiment in which he spins the spinner arrow and records the number it stops on. He repeats this action for a total of 30 times.

Question

Complete the statements about Jamison's experiment.
The theoretical probability of spinning a number greater than 5 is
50%
probability, Jamison should expect the arrow to stoppon a number greater than 5 approximately
15 times

Answer 1

To complete the statements about Jamison's experiment, we can follow these steps:

1. Identify the relevant outcomes: The numbers on the spinner range from 1 to 8. The numbers greater than 5 are 6, 7, and 8. Therefore, there are 3 outcomes that are greater than 5.

2. Calculate the theoretical probability: The total number of outcomes (sections of the spinner) is 8. The probability of spinning a number greater than 5 is the number of favorable outcomes divided by the total number of outcomes:

   \[ P(\text{Greater than 5}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{8} = 0.375 \text{ or } 37.5% \]

Based on this calculation, we can refine the statements:

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The theoretical probability of spinning a number greater than 5 is 37.5%.
Given this probability, Jamison should expect the arrow to stop on a number greater than 5 approximately 11 to 12 times in 30 spins.

(How to find this: Multiply the probability by the number of trials: \(30 \times \frac{3}{8} = 11.25\), which we can round to approximately 11 or 12 times.)

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So the completed statements would be:

• The theoretical probability of spinning a number greater than 5 is 37.5%.
• Given this probability, Jamison should expect the arrow to stop on a number greater than 5 approximately 11 to 12 times.