during one year in a school 5/8 of the students had measles, 1/2 had chicken pox and 1/8 had neither. what fraction of the school had both measles and chicken pox



show working

Let the fraction of those who had both be X

Then 5/8 + 1/2 + 1/8 - X = 1
(Since there are only 4 possible outcomes viz. Only measles,, only chicken pox, neither and both)

Now solve for X, that should be easy
Add all like terms on LHS to have
5/4 - X = 1
X = 5/4 - 1 = 1/4

Therefore, the fraction of those who had both diseases is 1/4