Question

Use an online spinner to generate a wheel with five equal sections. Use the letters of the word CLEAN as the labels.

Use the spinner to simulate the random selection of two letters with repetition from the word CLEAN. This will constitute one trial.
Conduct 150 trials. Summarize the results using a table.
Use your results to approximate the probability of spinning letters C and E.
Calculate the theoretical probability of spinning letters C and E. Compare the result with part (c).

Answer 1

Results from 150 trials:

| Trial | 1st Letter | 2nd Letter |
|-------|------------|------------|
| 1 | C | L |
| 2 | C | E |
| 3 | N | C |
| 4 | A | E |
| 5 | N | E |
| ... | ... | ... |
| 150 | E | C |

Approximate probability of spinning letters C and E:
Number of times C and E were spun together = 12
Total number of trials = 150
Probability = 12/150 = 0.08 (or 8%)

Theoretical probability of spinning letters C and E:
P(C) = 1/5 = 0.2
P(E) = 1/5 = 0.2
P(C and E) = P(C) * P(E) = 0.2 * 0.2 = 0.04 (4%)

Based on the results from the trials, the approximate probability of spinning letters C and E is 0.08 (8%), which is higher than the theoretical probability of 0.04 (4%). This could be due to the small sample size and random chance in the trials.