In a college, 30 students are taking a math class and 20 students are taking an English class. 5 students are taking both English and math. How many students are taking either English or math.

Answer 1

take out those five which are taking both, and you are left with 30+20-5=45 students taking either Math or English.

P(MorE)=Pr(M)+Pr(E)-Pr(M+E)
= (30/50)+(20/50)-5/50= 45/50

so if you pick a student at random, you have a probability of .90 of getting a student who is taking Math or English, but not both.