The letter tiles C, A, R, E

Question

, 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) 0.20 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) 0.25 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) 0.02 0.03 0.03 0.01 0.015

Answer 1

To develop a probability model based on Jorelle's observations, we need to calculate the probability of picking each letter tile based on their frequencies.

The frequencies observed were:

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

The total number of picks is 100 (as stated in the problem). The probability for each letter tile is calculated by dividing the frequency of that letter by the total number of picks.

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

Now, we can organize this into a probability model:

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

Thus, the correct response option is:

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

This model presents the probabilities rounded to two decimal places, as requested.