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: Count: 30/ Experimental %: 20.0%/ Theoretical %: 20.0%
L: Count: 26/ Experimental %: 17.3%/ Theoretical %; 20.0%
E: Count: 32/ Experimental %: 21.3%/ Theoretical %: 20.0%
A: Count: 31/ Experimental %: 20.7%/ Theoretical %: 20.0%
N: Count: 31/ Experimental %: 20.7%/ Theoretical %: 20.0%
c. Use your results to approximate the probability of spinning letters C and E.
Based on the results of the 150 trials, the experimental probability of spinning letters C and E together is 21.3%.
are you sure?
Apologies for the mistake in my previous response. Let's recalculate the probability of spinning letters C and E together based on the results of the 150 trials:
- The total number of trials where C and E were spun together: 32
- Total number of trials: 150
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 32/150
Probability = 0.2133 or 21.3%
Therefore, the correct experimental probability of spinning letters C and E together is 21.3%. Thank you for your patience.
d. Calculate the theoretical probability of spinning letters C and E. Compare
the result with part (c)
The theoretical probability of spinning letters C and E can be calculated as follows:
- The probability of spinning C: 1/5
- The probability of spinning E: 1/5
Since the events are independent, the probability of spinning C and E together is the product of their individual probabilities:
Probability(C and E) = Probability(C) * Probability(E)
Probability(C and E) = (1/5) * (1/5)
Probability(C and E) = 1/25
Therefore, the theoretical probability of spinning letters C and E together is 1/25 or 0.04 (4%).
Comparing this theoretical probability with the experimental probability calculated in part (c) of 21.3%, we can see that there is a significant difference. The experimental probability is much higher than the theoretical probability, indicating that the probability of spinning letters C and E together in this experiment is higher than what would be expected based on theoretical calculations.