To calculate the theoretical probability of spinning the letters C and E, we need to first determine the total number of segments on the spinner. This can be done by adding the number of segments for each letter:
- C: 8
- L: 7
- E: 3
- A: 6
- N: 6
Now let's sum these values:
\[ 8 + 7 + 3 + 6 + 6 = 30 \]
So, there are a total of 30 segments on the spinner.
Next, we'll find the probabilities of spinning C and E.
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Probability of spinning C: \[ P(C) = \frac{\text{Number of segments for C}}{\text{Total segments}} = \frac{8}{30} \]
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Probability of spinning E: \[ P(E) = \frac{\text{Number of segments for E}}{\text{Total segments}} = \frac{3}{30} \]
Now, if you want to find the probability of spinning either C or E (assuming they are individual events and we want the probability of one or the other occurring), we use the addition rule of probability:
\[ P(C \text{ or } E) = P(C) + P(E) = \frac{8}{30} + \frac{3}{30} = \frac{11}{30} \]
So, the theoretical probability of spinning C or E is \(\frac{11}{30}\).
Approximation
If part (c) involved an empirical method (like actual spins of the spinner), please provide the context or data so we can compare the theoretical result \(\frac{11}{30}\) with your empirical findings.