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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) 0.25 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 0.30 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) 0.02 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

1 answer

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

The frequencies given are:

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

Now, we calculate the probabilities:

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

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

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

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

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

Now, we can put these probabilities into a table format:

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

This gives us the probability model based on Jorelle's observations, rounded to the nearest hundredth.

Therefore, the correct response that matches this probability model is: \[ \text{X C A R E S P(X) } 0.20, 0.25, 0.30, 0.10, 0.15 \]