Probability problem with or/and (meaning of "neither").

Question

In a certain Algebra 2 class of 28 students, 5 of them play basketball and 21 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?

Does 'neither' mean 'not basketball AND not baseball'? Or 'not basketball OR not baseball'?

Answer 1

A student plays neither basketball nor baseball is an unambiguous way of saying that said student does not play basketball and does not play baseball.

Answer 2

The word neither means

not the one nor the other of two people or things; not either.

So, when the question says that the students play neither sport, it means they do not play baseball and does not play basketball.

Answer 3

5 students do not play at all. Therefore 23 students play at least one sport. Add numbers for both sport and get 26, so 3 students play both. So probability of student chosen at random plays both is 3/28.