Question
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.
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
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
Answers
GPT-4o mini
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:
---
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.)
---
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**.
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:
---
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.)
---
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**.