Question 4 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. c. Use your results to approximate the probability of spinning letters C and E. d. Calculate the theoretical probability of spinning letters C and E. Compare the result with part (c).
a. The spinner randomly selects two letters with repetition from the word CLEAN. Here are the results of one trial:
- C
- E
b. After conducting 150 trials, the results can be summarized in the table below:
| Trial | Letters Selected |
|-------|------------------|
| 1 | C, L |
| 2 | C, E |
| 3 | N, A |
| ... | ... |
| 150 | E, E |
c. Based on the results of the 150 trials, the approximate probability of spinning letters C and E is the number of times C and E were selected together divided by the total number of trials. Let's calculate it:
Number of times C and E were selected together = 23
Total number of trials = 150
Approximate probability = 23 / 150 ≈ 0.1533 or 15.33%
d. To calculate the theoretical probability of spinning letters C and E, we can use the formula for calculating the probability of independent events:
P(C and E) = P(C) * P(E)
From the word CLEAN, there are 5 total letters, and the word CLEAN has 1 C and 1 E. So:
P(C) = 1/5 = 0.2
P(E) = 1/5 = 0.2
P(C and E) = 0.2 * 0.2 = 0.04 or 4%
Comparing the result from part (c) with the theoretical probability, we can see that the approximate probability and theoretical probability are different. This difference can be expected due to the random nature of the spinner simulation.