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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

1.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

2.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

3.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

4.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 Jorelle's observed frequencies, we need to calculate the probability of each letter tile by dividing the frequency of each letter by the total number of trials (100).

Here are the observed frequencies:

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

To find the probabilities \( P(X) \), we perform the following calculations:

  1. Total number of trials: \( 20 + 25 + 30 + 10 + 15 = 100 \)

Now we calculate each probability:

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

Putting this information into the probability model:

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

Thus, the correct response based on the options provided is:

4.

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