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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 0.015X 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 0.15X 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) 0.25 0.25 0.35 0.15 0.15X 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 0.30 0.25 0.10 0.15X C A R E S P(X) 0.20 0.30 0.25 0.10 0.15
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1 answer

To develop a probability model based on Jorelle's observed frequencies of the letter tiles he picked, we need to calculate the probabilities for each letter.

Given the frequencies:

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

We first calculate the total number of picks, which is the sum of all the frequencies: \[ \text{Total} = 20 + 25 + 30 + 10 + 15 = 100 \]

Now we calculate the probability for each letter by dividing the frequency of each letter by the total number of picks (100):

  1. \( P(C) = \frac{20}{100} = 0.20 \)
  2. \( P(A) = \frac{25}{100} = 0.25 \)
  3. \( P(R) = \frac{30}{100} = 0.30 \)
  4. \( P(E) = \frac{10}{100} = 0.10 \)
  5. \( P(S) = \frac{15}{100} = 0.15 \)

Now we can express the probability model:

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

So the correct response is:

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

Thus the answer is: \( X \) C A R E S \( P(X) \) 0.20 0.25 0.30 0.10 0.15