To calculate the theoretical probability of spinning the letters C and E, we first need to determine the total number of letters on the spinner. Then we can find the probability of landing on C or E.
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Calculate the Total Number of Letters:
- C: 8
- L: 7
- E: 3
- A: 6
- N: 6
Total = C + L + E + A + N
Total = 8 + 7 + 3 + 6 + 6 = 30 -
Calculate the Probability of Spinning C: \[ P(C) = \frac{\text{Number of C}}{\text{Total number of letters}} = \frac{8}{30} = \frac{4}{15} \]
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Calculate the Probability of Spinning E: \[ P(E) = \frac{\text{Number of E}}{\text{Total number of letters}} = \frac{3}{30} = \frac{1}{10} \]
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Calculate the Probability of Spinning both C and E: Assuming we're looking for the probability of landing on either C or E in one spin (not spinning both at the same time), we add their probabilities: \[ P(C \text{ or } E) = P(C) + P(E) \] However, since C and E cannot occur simultaneously in a single spin, we don't need to worry about overlap.
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Probability of Spinning both C and E in two spins: Assuming two independent spins: \[ P(\text{C on first spin and E on second spin}) = P(C) \times P(E) \] \[ = \left(\frac{8}{30}\right) \times \left(\frac{3}{30}\right) = \frac{8 \times 3}{30 \times 30} = \frac{24}{900} = \frac{2}{75} \]
Conclusion:
- The theoretical probability of spinning C is \( \frac{4}{15} \).
- The theoretical probability of spinning E is \( \frac{1}{10} \).
- The combined probability of spinning C and E in two separate spins is \( \frac{2}{75} \).
If part (c) from your previous context involves approximating the probability of spinning both letters C and E, please provide that context for comparison.