Dependent and Independent Events - Portfolio
Use what you have learned about dependent and independent events. Apply
the formula for calculating the probability of events A and B.
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.
a. The spinner landed on the letters C and E.
b. Results after 150 trials:
Trial 1: C, E
Trial 2: L, A
Trial 3: E, N
...
Trial 150: C, E
c. Approximate probability of spinning letters C and E:
Number of times C and E were spun = 34
Total number of trials = 150
Probability = Number of times C and E were spun / Total number of trials
Probability = 34 / 150
Probability = 0.2267
Therefore, the approximate probability of spinning letters C and E is 0.2267.
d. Calculate the theoretical probability of spinning letters C and E. Compare
the result with part (c)
To calculate the theoretical probability of spinning letters C and E, we need to consider the total number of possible outcomes and the number of favorable outcomes where we spin C and E.
Total possible outcomes when spinning 2 letters with repetition from the word CLEAN:
There are 5 possible outcomes for each spin (C, L, E, A, N). Since we are spinning 2 letters, the total possible outcomes = 5 x 5 = 25.
Favorable outcomes where we spin C and E:
There is only 1 favorable outcome where we spin C and E.
Theoretical probability = Number of favorable outcomes / Total possible outcomes
Theoretical probability = 1 / 25
Theoretical probability = 0.04
The theoretical probability of spinning letters C and E is 0.04, which is significantly lower than the approximate probability calculated in part (c) (0.2267). This difference can be attributed to the fact that in the theoretical probability calculation, we are considering all possible outcomes equally likely, while in reality, the spinner may have biases or imperfections that affect the likelihood of certain outcomes.