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.
A- X C A R E S
P(X) 0.20 0.30 0.25 0.10 0.15
B- X C A R E S
P(X) 0.25 0.25 0.35 0.15 0.15
C- X C A R E S
P(X) 0.20 0.25 0.30 0.10 0.15
D- X C A R E S
P(X) 0.02 0.03 0.03 0.01 0.015
C- X C A R E S
P(X) 0.20 0.25 0.30 0.10 0.15
This probability model is based on the observed frequency given in the problem, with the probabilities calculated by dividing the frequency by the total number of trials (100). The probabilities are rounded to the nearest hundredth.
what percent?
To convert the probabilities to percent, we can multiply them by 100. So, the probabilities in the model become:
P(C) = 0.20 -> 20%
P(A) = 0.25 -> 25%
P(R) = 0.30 -> 30%
P(E) = 0.10 -> 10%
P(S) = 0.15 -> 15%
Therefore, the probability of selecting the letter C is 20%, the probability of selecting the letter A is 25%, and so on.
what about letter r?
To develop a probability model based on the observed frequency, we need to calculate the probability of each outcome. The probability of an outcome is given by the frequency of that outcome divided by the total number of trials (in this case, 100). Here's how you can calculate the probabilities for each outcome:
A- X C A R E S
P(X) 0.20 0.30 0.25 0.10 0.15
For outcome A, the frequency is 20, so the probability of selecting A is 20/100 = 0.20.
For outcome C, the frequency is 25, so the probability of selecting C is 25/100 = 0.25.
For outcome R, the frequency is 30, so the probability of selecting R is 30/100 = 0.30.
For outcome E, the frequency is 10, so the probability of selecting E is 10/100 = 0.10.
For outcome S, the frequency is 15, so the probability of selecting S is 15/100 = 0.15.
So the probability model for this experiment is:
P(A) = 0.20
P(C) = 0.25
P(R) = 0.30
P(E) = 0.10
P(S) = 0.15
Note: It is important to remember that the probabilities should add up to 1. In this case, 0.20 + 0.25 + 0.30 + 0.10 + 0.15 = 1, which confirms that the probabilities are correctly calculated.