1. A color for which the experimental probability is closest to the theoretical probability is: A. Brown; The experimental probability is 19.52%, and the theoretical probability is 20%.
2. A color for which the difference between the theorectical probability and experimental probability is greatest is: C. Yellow; The experimental probability is 16.96%, and the theoretical probability is 20%.
Assuming all the five colors have the same probability of being the outcome, the theoretical probability for each color can be calculated as follows;
Theoretical probability = 1/5
Theoretical probability = 0.20 × 100.
Theoretical probability = 20%.
Next, we would determine the total number of colors by adding the frequencies together as follows;
Total number of colors = 118 + 137 + 122 + 106 + 142
Total number of colors = 625 colors.
Part 1.
The experimental probability is the quotient of the number of times each color appears and the total number of spins:
Orange:
P(O) = 118/625
P(O) = 0.1888 × 100 = 18.88%.
Purple:
P(Pu) = 137/625
P(Pu) = 0.2192 × 100 = 21.92%
Brown:
P(B) = 122/625
P(B) = 0.1952 × 100 = 19.52%
Yellow:
P(Y) = 106/625
P(Y) = 1.696 × 100 = 16.96%.
Green:
P(G) = 142/625
P(G) = 0.2272 × 100 = 22.72%
Therefore, color brown is closest because 19.52% is closest to 20%.
Part 2.
In conclusion, Yellow is a color for which the difference between the theorectical probability and experimental probability is greatest because the experimental probability is 16.96%, and the theoretical probability is 20%.
Missing information:
A game of chance has a spinner with five equal-sized sections. The results of 625 spins are shown below:
Color. Frequency
Orange. 118
Purple. 137
Brown. 122
Yellow. 106
Green. 142