Question

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) 0.20 0.30 0.25 0.10 0.15
Table with 6 columns and 2 rows.Row 1: Column 1, 'X'; Column 2, 'C'; Column 3, 'A'; Column 4, 'R'; Column 5, 'E'; Column 6, 'S' Row 2: Column 1, 'P(X)'; Column 2, '0.20'; Column 3, '0.30'; Column 4, '0.25'; Column 5, '0.10'; Column 6, '0.15'

X C A R E S
P(X) 0.02 0.03 0.03 0.01 0.015
Table with 6 columns and 2 rows.Row 1: Column 1, 'X'; Column 2, 'C'; Column 3, 'A'; Column 4, 'R'; Column 5, 'E'; Column 6, 'S' Row 2: Column 1, 'P(X)'; Column 2, '0.02'; Column 3, '0.03'; Column 4, '0.03'; Column 5, '0.01'; Column 6, '0.015'

X C A R E S
P(X) 0.25 0.25 0.35 0.15 0.15
Table with 6 columns and 2 rows.Row 1: Column 1, 'X'; Column 2, 'C'; Column 3, 'A'; Column 4, 'R'; Column 5, 'E'; Column 6, 'S' Row 2: Column 1, 'P(X)'; Column 2, '0.25'; Column 3, '0.25'; Column 4, '0.35'; Column 5, '0.15'; Column 6, '0.15'

X C A R E S
P(X) 0.20 0.25 0.30 0.10 0.15
Table with 6 columns and 2 rows.Row 1: Column 1, 'X'; Column 2, 'C'; Column 3, 'A'; Column 4, 'R'; Column 5, 'E'; Column 6, 'S' Row 2: Column 1, 'P(X)'; Column 2, '0.20'; Column 3, '0.25'; Column 4, '0.30'; Column 5, '0.10'; Column 6, '0.15'

Answer 1

Probability = frequency/100. So

P(C) = 20/100 = 0.20
P(A) = 25/100 = 0.25
P(R) = 30/100 = 0.30
P(E) = 10/100 = 0.10
P(S) = 15/100 = 0.15

(The fourth response is correct.)