Solving a Probability Question ## A student goes to the library. The probability that she checks out (a) a work of fiction is 0.40, (b) a work of non-fiction is 0.40,and (c) both fiction and non-fiction is 0.20. What is the probability that the student checks out a work of fiction, non-fiction, or both? I am trying to understand how I can do it, but all i came up with was: Probability of (checking out with fiction or non-fiction)= 0.4+0.4= 0.80 Probability of (checking out with both )= 0.80-0.20= 0.60 Is this correct and if not what is the correct answer and why?

The wording of the problem is not optimal. It should say something like "The probability that among the books she checks out there is at least one fiction book is $0.4$." And so on for the others. With that interpretation, your calculation is right.

To be very formal, let $A$ be the event that she checks out at least one fiction book, and let $B$ be the event she checks out at least one non-fiction book. We want $\Pr(A\cup B)$. We have in general $$\Pr(A\cup B)=\Pr(A)+\Pr(B)-\Pr(A\cap B).$$ Thus in our case we have $\Pr(A\cup B)=0.4+0.4-0.2$.