Question

A game has a spinner with 8 equal- sized sections. The results of 450 spins are shown in the table. Part Frequency 1 58 2 52 3 39 4 77 5 50 6 43 7 60 8 71

For Which Number is the number difference between the theoretical probability and experimental probability greatest?Explain

Answer 1

The theoretical probability of each section is 1/8, since there are 8 equal-sized sections on the spinner. To find the theoretical frequency, we multiply the theoretical probability by the total number of spins:

Theoretical frequency = (1/8) x 450 = 56.25

We can then calculate the experimental probability for each section by dividing the frequency by the total number of spins:

Experimental probability = Frequency/Total number of spins

Using this formula, we can calculate the experimental probabilities for each section:

Part 1: Experimental probability = 58/450 ≈ 0.129

Part 2: Experimental probability = 52/450 ≈ 0.116

Part 3: Experimental probability = 39/450 ≈ 0.087

Part 4: Experimental probability = 77/450 ≈ 0.171

Part 5: Experimental probability = 50/450 ≈ 0.111

Part 6: Experimental probability = 43/450 ≈ 0.096

Part 7: Experimental probability = 60/450 ≈ 0.133

Part 8: Experimental probability = 71/450 ≈ 0.158

To find the number with the greatest difference between the theoretical and experimental probability, we can calculate the difference between the two probabilities for each section:

Part 1: |0.125 - 0.129| = 0.004

Part 2: |0.125 - 0.116| = 0.009

Part 3: |0.125 - 0.087| = 0.038

Part 4: |0.125 - 0.171| = 0.046

Part 5: |0.125 - 0.111| = 0.014

Part 6: |0.125 - 0.096| = 0.029

Part 7: |0.125 - 0.133| = 0.008

Part 8: |0.125 - 0.158| = 0.033

As we can see, the greatest difference between the theoretical and experimental probability is for Part 4 with a difference of 0.046. This indicates that the experimental frequency for Part 4 is significantly different from the theoretical frequency, which may suggest that the spinner is biased towards that section.