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 afternoon classes given he or she is a senior. Round to the nearest thousandth. (1 point)
0.184
0.395
0.116
0.464
To find the probability that the student preferred afternoon classes given he or she is a senior, you need to use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
where:
- P(A|B) is the probability of event A given event B has occurred
- P(A and B) is the probability of both events A and B happening
- P(B) is the probability of event B happening
In this case, event A is a student preferring afternoon classes and event B is a student being a senior.
From the table, we can see that 62 out of 200 seniors preferred afternoon classes. So, P(A and B) = 62/200.
Also, there are 134 seniors out of a total of 400 students, so P(B) = 134/400.
Now, we can plug these values into the formula to find the probability:
P(A|B) = (62/200) / (134/400)
P(A|B) = (62/200) * (400/134)
P(A|B) = 0.464
Therefore, the probability that a student preferred afternoon classes given he or she is a senior is 0.464 (rounded to the nearest thousandth).