A class of 20 boys and 10 girls has 15 Math majors and 15 Physics students. What is the probability of picking a student who is both a boy and a physics major? A physics major and a girl?

Answer 1

There is not a unique solution to this problem.

Here are two possibilities, assuming that there are no math majors that are also physics students, and that every student is one or the other (This is not specified in the problem, but it's more restrictive, so if there are multiple solutions with the extra assumption in place, there are at least as many without the restriction. Also, the problem is somewhat poorly worded in that it appears to interchange physics student with physics major)

1) There is 1 girl physics student, 9 girl math majors, 14 boy physics students, and 6 boy math majors. With the assumption of no overlap between math majors and physics students, all the conditions hold: 20 boys, 10 girls, 15 math majors, 15 physics students.

2) There are 2 girl physics students, 8 girl math majors, 13 boy physics students, and 7 boy math majors. All the conditions hold: there are 20 boys, 10 girls, 15 math majors, 15 physics students.