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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) 0.20 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
X C A R E S P(X) 0.25 0.25 0.35 0.15 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 0.25 0.30 0.10 0.15

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
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1 answer

To develop a probability model based on Jorelle's observed results, we need to calculate the probability of each letter being picked. The total number of picks is 100, and the frequency of each letter is given as follows:

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

The probability \( P(X) \) of each letter can be calculated using the formula:

\[ P(X) = \frac{\text{Frequency of } X}{\text{Total Observations}} \]

Given that the total number of observations is 100, we can calculate each probability:

  1. For C: \[ P(C) = \frac{20}{100} = 0.20 \]

  2. For A: \[ P(A) = \frac{25}{100} = 0.25 \]

  3. For R: \[ P(R) = \frac{30}{100} = 0.30 \]

  4. For E: \[ P(E) = \frac{10}{100} = 0.10 \]

  5. For S: \[ P(S) = \frac{15}{100} = 0.15 \]

From this, we can compile the probabilities into a model:

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

Thus, the correct probability model is:

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

Based on the provided options, the correct response is:

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