Each person in a group of students was identified by year and asked when he or she preferred taking classes: in the morning, afternoon, or evening. The results are shown in the table. Find the probability that the student preferred morning classes given he or she is a freshman. Round your answer to the nearest thousandth.
Freshman Sophomore Junior Senior
Morning: 19 2 6 16
Afternoon: 17 3 13 15
Evening: 8 14 9 7
There are 19 freshman who preferred morning classes out of a total of 50 students. So the probability is:
P(morning class | freshman) = 19/50 ≈ 0.380
Rounded to the nearest thousandth, the answer is 0.380.
To find the probability that a student preferred morning classes given that they are a freshman, we need to divide the number of freshmen who prefer morning classes by the total number of freshmen in the group.
From the table, we can see that there are 19 freshmen who prefer morning classes.
To find the total number of freshmen, we need to sum up the number of freshmen in each class preference category. From the table, we can see that there are:
- 19 freshmen who prefer morning classes
- 17 freshmen who prefer afternoon classes
- 8 freshmen who prefer evening classes
Therefore, the total number of freshmen is 19 + 17 + 8 = 44.
To find the probability, we divide the number of freshmen who prefer morning classes (19) by the total number of freshmen (44):
Probability of a freshman preferring morning classes = 19 / 44
Rounded to the nearest thousandth, the probability is approximately 0.432.
To find the probability that a student preferred morning classes given that he or she is a freshman, we need to use conditional probability.
The conditional probability formula is:
P(A|B) = P(A ∩ B) / P(B)
In this case, event A is the student preferring morning classes and event B is the student being a freshman.
Step 1: Calculate P(A ∩ B), the probability that a student prefers morning classes and is a freshman. Looking at the table, we can see that 19 freshmen preferred morning classes. So, P(A ∩ B) = 19.
Step 2: Calculate P(B), the probability that a student is a freshman. Looking at the table, we can see that there are a total of 46 freshmen. So, P(B) = 46.
Step 3: Use the conditional probability formula to find P(A|B):
P(A|B) = P(A ∩ B) / P(B)
P(A|B) = 19 / 46
P(A|B) ≈ 0.413
Therefore, the probability that a student preferred morning classes given that he or she is a freshman is approximately 0.413 (rounded to three decimal places).