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
0.464
0.395
0.116
To find the probability that the student preferred afternoon classes given he or she is a senior, you need to use the conditional probability formula:
P(afternoon | senior) = P(afternoon and senior) / P(senior)
From the table, we can see that the number of seniors who preferred afternoon classes is 23, and the total number of seniors is 65. So P(afternoon and senior) = 23/65.
The total number of students who preferred afternoon classes is 102, and the total number of students is 260. So P(senior) = 102/260.
Now plug in the values:
P(afternoon | senior) = (23/65) / (102/260)
P(afternoon | senior) = (23/65) * (260/102)
P(afternoon | senior) ≈ 0.584
Rounded to the nearest thousandth, the probability that the student preferred afternoon classes given he or she is a senior is 0.584.