Th e letters C, A, R, E, and S are placed in a box. Joelle picks a letter from the box and records the result before placing it back. He repeats the procedure 100 times and observes the following result. OUTCOME C A R E S, FREQUENCY C 20,A 25,R 30,E 10,S 15. Based on the observed FREQUENCY, develop a probability model for this experiment
The probability model for this experiment is as follows:
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
The sum of all probabilities must be equal to 1.
To develop a probability model based on the observed frequency, we need to calculate the probability of each letter appearing.
The total number of trials is given as 100. The frequency of each letter represents how many times that letter appeared in the 100 trials.
Let's calculate the probability for each letter:
Probability of selecting C = Frequency of C / Total Number of Trials = 20 / 100 = 0.2
Probability of selecting A = Frequency of A / Total Number of Trials = 25 / 100 = 0.25
Probability of selecting R = Frequency of R / Total Number of Trials = 30 / 100 = 0.3
Probability of selecting E = Frequency of E / Total Number of Trials = 10 / 100 = 0.1
Probability of selecting S = Frequency of S / Total Number of Trials = 15 / 100 = 0.15
Therefore, the probability model for this experiment is:
C: 0.2
A: 0.25
R: 0.3
E: 0.1
S: 0.15