To determine the probabilities and the total number of spins for each color in Davis's spinner experiment, we need to follow these steps:
1. Calculate the Total Number of Spins:
The experiment recorded frequencies for four colors: Red, Green, Blue, and Purple. The frequencies are provided as:
- Red: 5
- Green: 5
- Blue: 8
- Purple: 2
To find the total number of spins, add up the frequencies of each color:
[tex]\[
\text{Total Spins} = \text{Frequency of Red} + \text{Frequency of Green} + \text{Frequency of Blue} + \text{Frequency of Purple}
\][/tex]
[tex]\[
\text{Total Spins} = 5 + 5 + 8 + 2 = 20
\][/tex]
2. Calculate the Probability for Each Color:
The probability of landing on a specific color is calculated by dividing the frequency of that color by the total number of spins.
- Probability of landing on Red:
[tex]\[
P(\text{Red}) = \frac{\text{Frequency of Red}}{\text{Total Spins}} = \frac{5}{20} = 0.25
\][/tex]
- Probability of landing on Green:
[tex]\[
P(\text{Green}) = \frac{\text{Frequency of Green}}{\text{Total Spins}} = \frac{5}{20} = 0.25
\][/tex]
- Probability of landing on Blue:
[tex]\[
P(\text{Blue}) = \frac{\text{Frequency of Blue}}{\text{Total Spins}} = \frac{8}{20} = 0.40
\][/tex]
- Probability of landing on Purple:
[tex]\[
P(\text{Purple}) = \frac{\text{Frequency of Purple}}{\text{Total Spins}} = \frac{2}{20} = 0.10
\][/tex]
By completing these steps, we find the following results:
- The total number of spins is 20.
- The probability of landing on Red is 0.25 (25%).
- The probability of landing on Green is 0.25 (25%).
- The probability of landing on Blue is 0.40 (40%).
- The probability of landing on Purple is 0.10 (10%).
These calculations provide a clear understanding of how frequently each color appeared in Davis's spinner experiment and the corresponding probabilities of landing on each color.
