A game has a spinner with 6 equal-sized sections. The results of 350 spins are shown in the table.

Question

Part Frequency
1 27
2 44
3 52
4 32
5 40
6 55

Part A

For which part is the experimental probability closest to the theoretical probability? Explain.

Part

The experimental probability is
% and the theoretical probability is
%.

Part B

For which part is the difference between the theoretical probability and experimental probability greatest? Explain.

Part

The difference between the experimental probability and the theoretical probability is
%. This is greater than the differences for the other parts.

Answer 1

Part A:
Based on the table, we can calculate the experimental probability for each part by dividing the frequency of that part by the total number of spins (350). The theoretical probability for each part would be 1/6 since there are 6 equal-sized sections on the spinner.

Part 1: Experimental probability = 27/350 ≈ 0.077, Theoretical probability = 1/6 ≈ 0.167

Part 2: Experimental probability = 44/350 ≈ 0.126, Theoretical probability = 1/6 ≈ 0.167

Part 3: Experimental probability = 52/350 ≈ 0.149, Theoretical probability = 1/6 ≈ 0.167

Part 4: Experimental probability = 32/350 ≈ 0.091, Theoretical probability = 1/6 ≈ 0.167

Part 5: Experimental probability = 40/350 ≈ 0.114, Theoretical probability = 1/6 ≈ 0.167

Part 6: Experimental probability = 55/350 ≈ 0.157, Theoretical probability = 1/6 ≈ 0.167

Comparing the experimental probabilities to the theoretical probability, we can see that the experimental probability for Part 1 is closest to the theoretical probability.

Part B:
To find the difference between the theoretical probability and experimental probability for each part, we subtract the theoretical probability from the experimental probability.

Part 1: |0.077 - 0.167| ≈ 0.090

Part 2: |0.126 - 0.167| ≈ 0.041

Part 3: |0.149 - 0.167| ≈ 0.018

Part 4: |0.091 - 0.167| ≈ 0.076

Part 5: |0.114 - 0.167| ≈ 0.053

Part 6: |0.157 - 0.167| ≈ 0.010

The largest difference between theoretical probability and experimental probability is for Part 1 (0.090), making it the greatest difference among all the parts.