Problem:
In a new school percent of the students are freshmen, percent are sophomores, percent are juniors, and percent are seniors. All freshmen are required to take Latin, and percent of the sophomores, percent of the juniors, and percent of the seniors elect to take Latin. The probability that a randomly chosen Latin student is a sophomore is , where and are relatively prime positive integers. Find .
Solution:
Without loss of generality it may be assumed that there are students in the school. Then the students taking Latin consist of freshman, sophomores, juniors, and seniors. The required probability is the number of sophomores taking Latin divided by the number of students taking Latin or . The requested sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions