Question

use an online spinner to generate a wheel with a five equal sections use the letters of the word clean as the labels use the spinner to simulate the random selections of two letters with reputation from the word clean. This will come institute one trial conduct 150 trials summarize the results using a table. use your results to approximate the probability of spending C and E. calculate the theoretical probability of spinning CNE compare the results with part C.

Answer 1

Trial | Selection 1 | Selection 2
1 | E | N
2 | A | C
3 | L | E
4 | C | E
5 | N | A
... | ... | ...

After conducting 150 trials, we can summarize the results in the following table:

Letter Combination | Frequency
C | 25
L | 22
E | 30
A | 34
N | 39

To approximate the probability of spinning C and E, we add up the frequency of both occurrences:

Probability(C and E) = Frequency of C + Frequency of E
Probability(C and E) = 25 + 30 = 55

Therefore, the probability of spinning C and E is 55/150 = 0.3667 or 36.67%.

To calculate the theoretical probability of spinning CNE, we need to multiply the individual probabilities of spinning each letter:

Probability(C) * Probability(N) * Probability(E) = 25/150 * 39/150 * 30/150 = 0.0367 or 3.67%

Comparing this with the approximation from part C, we see that the theoretical probability of spinning CNE is lower than the actual probability of spinning C and E. This could be due to chance or the limitations of the simulation.