To develop a probability model based on Jorelle's observations of the letter tiles, we need to calculate the probability for each letter based on the recorded frequencies.
The frequencies given are:
- C: 20
- A: 25
- R: 30
- E: 10
- S: 15
Total frequency of all letters combined: \[ 20 + 25 + 30 + 10 + 15 = 100 \]
Next, we calculate the probability \( P(X) \) for each letter by dividing its frequency by the total frequency (100):
- \( P(C) = \frac{20}{100} = 0.20 \)
- \( P(A) = \frac{25}{100} = 0.25 \)
- \( P(R) = \frac{30}{100} = 0.30 \)
- \( P(E) = \frac{10}{100} = 0.10 \)
- \( P(S) = \frac{15}{100} = 0.15 \)
Thus, the probability model can be summarized as follows:
\[ \begin{array}{|c|c|c|c|c|c|} \hline X & C & A & R & E & S \ \hline P(X) & 0.20 & 0.25 & 0.30 & 0.10 & 0.15 \ \hline \end{array} \]
Therefore, the correct probability model based on the observed frequency is:
- \( P(X) \) for each letter:
- \( C: 0.20 \)
- \( A: 0.25 \)
- \( R: 0.30 \)
- \( E: 0.10 \)
- \( S: 0.15 \)
Among the options given, the correct one corresponds to:
X C A R E S
P(X) 0.20 0.25 0.30 0.10 0.15