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The letter tiles C, A, R, E

, and S
are placed in a box. Without looking, Jorelle picks a letter tile from the box and records the result before placing it back. He repeats the procedure 100 times and observes the following results:

The table presents the frequency of occurrences for letters C, A, R, E, and S when Jorelle picks them from the box.
Outcomes C A R E S
Frequency 20 25 30 10 15
Based on the observed frequency, develop a probability model for this experiment. Express the probability in decimal form, rounded to the nearest hundredth.

(1 point)
Responses

X C A R E S
P(X) 0.02 0.03 0.03 0.01 0.015
X C A R E S P(X) 0.02 0.03 0.03 0.01 0.015

X C A R E S
P(X) 0.20 0.25 0.30 0.10 0.15
X C A R E S P(X) 0.20 0.25 0.30 0.10 0.15

X C A R E S
P(X) 0.20 0.30 0.25 0.10 0.15
X C A R E S P(X) 0.20 0.30 0.25 0.10 0.15

X C A R E S
P(X) 0.25 0.25 0.35 0.15 0.15

1 answer

To develop a probability model based on the observed frequencies, we need to calculate the probability for each letter. The probabilities can be calculated by dividing the frequency of each letter by the total number of trials (in this case, 100).

The observed frequencies are:

  • C: 20
  • A: 25
  • R: 30
  • E: 10
  • S: 15

  1. Calculate Total Frequency: \[ \text{Total} = 20 + 25 + 30 + 10 + 15 = 100 \]

  2. Calculate Probabilities:

    • \( P(C) = \frac{20}{100} = 0.20 \)
    • \( P(A) = \frac{25}{100} = 0.25 \)
    • \( P(R) = \frac{30}{100} = 0.30 \)
    • \( P(E) = \frac{10}{100} = 0.10 \)
    • \( P(S) = \frac{15}{100} = 0.15 \)

The resulting probability model is:

\[ \begin{array}{|c|c|c|c|c|c|} \hline X & C & A & R & E & S \ \hline P(X) & 0.20 & 0.25 & 0.30 & 0.10 & 0.15 \ \hline \end{array} \]

Thus, the correct response from the options provided is: \[ X \quad C \quad A \quad R \quad E \quad S \ P(X) \quad 0.20 \quad 0.25 \quad 0.30 \quad 0.10 \quad 0.15 \]