The greatest possible number of students taken both exams

[Guest]

Hi everyone please provide me the solution for the following problems on probability.Also please give me the valid and good explanation for the how you are arriving to the answers.Actually i am not finding good explanation for these problems in the book.

In a graduation class of 236 students,142 took algebra and 121 took chemistry. What is the greatest possible number of students that could have taken
both algebra and chemistry?

Thanks,
S.

[Guest]

Hi!

If you want the greatest possible number of students who took both, you want to assume that as many students as possible didn't take neither algebra nor chemistry. So let's say all 121 chemistry students also took algebra:

121 students took chemistry + algebra
(142 - 121) = 21 students took just algebra
(236 - 142) = 94 students didn't take either
(121 + 21 + 94) = 236 students

So the max possible number of students who took both is 121 students

[Guest]

I would say that "a maximum of 121 students took both" is obvious! A much more interesting problem would be "what is the minimum number of students who took both".