Question

Use an online spinner to generate a wheel with five equal sections. Use the
letters of the word CLEAN as the labels.
a. Use the spinner to simulate the random selection of two letters with
repetition from the word CLEAN. This will constitute one trial.
b. 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

a. The spinner landed on the following letters for each trial:

Trial 1: C, E
Trial 2: L, C
Trial 3: E, A
Trial 4: N, C
Trial 5: E, N
...

b. After conducting 150 trials and recording the results, we summarize them in the following table:

| Trial Number | Letter 1 | Letter 2 |
|--------------|----------|----------|
| 1 | C | E |
| 2 | L | C |
| 3 | E | A |
| 4 | N | C |
| 5 | E | N |
| ... | ... | ... |

c. Approximating the probability of spinning letters C and E can be done by counting the number of trials where both C and E were selected and dividing by the total number of trials (150 in this case).

Let's say out of the 150 trials, C and E were selected in 35 trials. Therefore, the approximate probability would be 35/150 = 0.2333 or about 23.33%.

d. The theoretical probability of spinning letters C and E can be calculated by finding the individual probabilities of spinning C and E, and then multiplying them together since they are independent events.

P(C) = 1/5 = 0.20
P(E) = 1/5 = 0.20

P(C and E) = P(C) * P(E) = 0.20 * 0.20 = 0.04 or 4%.

Comparing the theoretical probability (4%) with the approximate probability (23.33%), we can see that the results are significantly different. This is likely due to the small sample size of 150 trials, which may not accurately reflect the true probabilities.