In a certain Algebra 2 class of 23 students, 7 of them play basketball and 12 of them play baseball. There are 9 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?
It depends upon what you mean by "or":
1) Inclusive or: it means one or the other and possibly both.
2) Exclusive or: it means one or the other but not both.
There are 23 students
-- 9 students play neither sport
-- therefore, 23 - 9 = 14 students play at least one of the two sports; some play both sports.
Inclusive or: the probability will be: 14 / 23 that a student chosen at random will play at least one of the two sports.
Exclusive or: we need to first find how many students play both sports.
Since 14 persons play sports and since 7 play basketball and 12 play baseball, this requires 7 + 12 = 19 students.
Subtracting 19 - 14 = 5 give the number of students who play both sports.
If we eliminate these 5 persons as well as the 9 who play neither sport, we have to eliminate 5 + 9 = 14 persons.
This gives 23 - 14 = 9 persons who play only one of the two sports.
The probability will be: 9/23 play a sport, but only one sport.