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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 0.25 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) 0.20 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

1 answer

To develop a probability model based on the observed frequencies, we first need to calculate the total number of picks, which is given as 100. The probabilities of each letter can be calculated by dividing the frequency of each letter by the total number of picks.

Here's the frequency breakdown:

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

Now, we calculate the probabilities:

  1. Probability of picking C (P(C)) = Frequency of C / Total picks = 20 / 100 = 0.20
  2. Probability of picking A (P(A)) = Frequency of A / Total picks = 25 / 100 = 0.25
  3. Probability of picking R (P(R)) = Frequency of R / Total picks = 30 / 100 = 0.30
  4. Probability of picking E (P(E)) = Frequency of E / Total picks = 10 / 100 = 0.10
  5. Probability of picking S (P(S)) = Frequency of S / Total picks = 15 / 100 = 0.15

So the probability model is:

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

The correct response from the provided options is:

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