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:
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.
The probability of selecting each letter can be found by dividing the frequency by the total number of trials:
- P(C) = 20/100 = 0.2
- P(A) = 25/100 = 0.25
- P(R) = 30/100 = 0.3
- P(E) = 10/100 = 0.1
- P(S) = 15/100 = 0.15
We can check that these probabilities add up to 1:
0.2 + 0.25 + 0.3 + 0.1 + 0.15 = 1
Therefore, the probability model for this experiment is:
- P(C) = 0.2
- P(A) = 0.25
- P(R) = 0.3
- P(E) = 0.1
- P(S) = 0.15
To develop a probability model based on the observed frequency, we need to divide the frequency of each outcome by the total number of trials, which is 100.
Outcome Frequency Probability
C 20 20/100 = 0.2
A 25 25/100 = 0.25
R 30 30/100 = 0.3
E 10 10/100 = 0.1
S 15 15/100 = 0.15
Rounded to the nearest hundredth, the probability model for this experiment is:
C: 0.20
A: 0.25
R: 0.30
E: 0.10
S: 0.15
To develop a probability model based on the observed frequency, we need to find the probability of each outcome (picking each letter tile) by dividing the frequency of each outcome by the total number of trials (100). Let's calculate the probabilities for each letter tile:
Probability of picking C: 20/100 = 0.2
Probability of picking A: 25/100 = 0.25
Probability of picking R: 30/100 = 0.3
Probability of picking E: 10/100 = 0.1
Probability of picking S: 15/100 = 0.15
Rounding each probability to the nearest hundredth, the probability model for this experiment is:
C: 0.20
A: 0.25
R: 0.30
E: 0.10
S: 0.15