Question

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

First note: the frequencies given (27+44+52+32+40+55 = 250) add to 250, not 350. I’ll use the given frequencies (total 250). If the total really is 350, please provide the missing data.

Theoretical probability for any part = 1/6 ≈ 16.67%.

Experimental percentages (frequency ÷ 250):
- Part 1: 27/250 = 10.8%
- Part 2: 44/250 = 17.6%
- Part 3: 52/250 = 20.8%
- Part 4: 32/250 = 12.8%
- Part 5: 40/250 = 16.0%
- Part 6: 55/250 = 22.0%

Part A
- Closest to theoretical: Part 5.
- Experimental = 16.0% and theoretical = 16.67% (difference = 0.67%), which is the smallest difference.

Part B
- Largest difference from theoretical: Part 1.
- Difference = |10.8% − 16.67%| = 5.87%, which is greater than the differences for the other parts.