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?
 A: 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 $\Pr(A\cup B)=0.4+0.4-0.2$.
A: The question is ambiguous. The probabilities are stated in a way that makes it seem that the probability that the student checks out a single nonfiction book is $0.4,$ and similarly, the probability that the student checks out a single fiction book is $0.4.$ If we consider it in this way, the probability is in fact $0.4 \times 2 + 0.2 = \boxed{1}.$
But perhaps the question meant to read as the probability of getting at least one nonfiction book being $0.4$ and similarly with the fiction. In this case, we apply Principle of Inclusion and Exclusion, and you would be correct.
