To calculate the theoretical probability of spinning letters C and E, we first need to determine the total number of letters and the frequency of each letter.
From your data:
- C: 8
- L: 7
- E: 3
- A: 6
- N: 6
Step 1: Calculate the total number of letters.
Total = C + L + E + A + N Total = 8 + 7 + 3 + 6 + 6 = 30
Step 2: Calculate the probability of spinning each letter.
- Probability of spinning C (P(C)) = Number of C's / Total letters = 8 / 30
- Probability of spinning E (P(E)) = Number of E's / Total letters = 3 / 30
Step 3: Calculate the probability of spinning both letters C and E.
Assuming that each spin is independent, the probability of spinning C and then E is:
P(C and E) = P(C) * P(E)
So,
P(C and E) = (8/30) * (3/30) = 24 / 900 = 1 / 37.5
The theoretical probability of spinning both letters C and E is approximately \(0.0267\) (or 2.67%).
Compare with part (c):
Without specific results provided from part (c), I cannot directly compare the value, but you can now compare your approximation from your actual spins (in part c) with this theoretical probability to see how close they are.
If you have results from part (c), please share them and we can analyze the comparison further!