Calculate the frequency that the spinner landed on a pink sector.
(experimental probability)
1 : Blue
2 : Green
3 : Green
4 : Blue
5 : Blue
6 : Orange
7 : Pink
8 : Green
9 : Blue
10: Orange
11: Green
12: Orange
13: Orange
14: Pink
15: Blue
16: Yellow
17: Blue
18: Pink
19: Blue
20: Green
There are a total of 20 spins, and the spinner landed on a pink sector 2 times (at positions 7 and 18).
Therefore, the experimental probability of the spinner landing on a pink sector is:
Frequency of pink / Total number of spins = 2 / 20 = 0.1
So, the experimental probability of the spinner landing on a pink sector is 0.1 or 10%.
Are the values for part (1) and part (3) the same?
Why or why not? (use complete sentences)
No, the values for part (1) and part (3) are not the same. In part (1), we calculated the experimental probability of the spinner landing on a pink sector by counting how many times the spinner landed on pink out of a total of 20 spins. This is an example of experimental probability, which is based on the results of actual experiments or observations.
In part (3), we calculated the theoretical probability of the spinner landing on a pink sector by dividing the number of pink sectors on the spinner by the total number of sectors on the spinner. Theoretical probability is based on mathematical reasoning and does not involve actual experiments.
Since experimental probability is based on observed results, it can vary from trial to trial. The values for experimental probability and theoretical probability can be different because theoretical probability is based on idealized assumptions and calculations, while experimental probability is based on actual outcomes from experiments.
If we theoretically predicted that the spinner landed on pink 5 times but it experimentally landed on pink two times
Are the values for the theoretical prediction and the experimental results the same?
Why or why not? (use 1-2 sentences)