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:

Question

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) 0.02 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) 0.25 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
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Answer 1

To develop a probability model based on Jorelle's observed frequencies for the letters C, A, R, E, and S, we first need to convert the frequencies into probabilities.

The total number of picks was 100. The formula to calculate the probability for each letter is:

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

Using the provided frequencies:

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

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

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

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

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

Now, we can organize this information into a probability model:

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

Therefore, the correct probability model based on the observed results is:

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

This corresponds with the option that states:

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