To find the probability that a student preferred afternoon classes given he or she is a junior, we need to use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
In this case, A represents the student preferring afternoon classes and B represents the student being a junior.
The number of juniors who preferred afternoon classes is 13. The total number of juniors is 6 + 13 + 9 = 28.
So, P(A and B) = 13/28
The probability of a student being a junior is 28/100 since there were 100 students total.
So, P(B) = 28/100
Therefore, the probability that a student preferred afternoon classes given he or she is a junior is:
P(A|B) = (13/28) / (28/100)
P(A|B) = 0.464
Therefore, the probability that a student preferred afternoon classes given he or she is a junior is 0.464.
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 junior. Round to the nearest thousandth.
Freshman Sophomore Junior Senior
Morning 19 2 6 16
Afternoon 17 3 13 15
Evening 8 14 9 7
(1 point)
Responses
0.571
0.571
0.464
0.464
0.342
0.342
0.158
0.158
1 answer