Need help finding the intersection of two probable events A study is conducted on kids about what stuffed animals they have, $15\%$ of the kids don't have a stuffed animal, $50\%$ have a stuffed dog and $55\%$ have a stuffed bear. If one of the children is chosen randomly, what is the probability that a student has a stuffed bear and a stuffed dog? I'm confused because I don't know how to find the intersection between the events of a child having a stuffed bear and a stuffed dog. How would I go about solving a problem like this?

Let $A$ be a child has a stuffed dog. Let $B$ be a student has a stuffed bear.

You know $Pr(A)$, $Pr(B)$ and $Pr(\bar{A}\bar{B})$.

If you sketch out a Venn diagram, the following relationship will be easier to see.

$$1 = Pr(A) + Pr(B) - Pr(AB) + Pr(\bar{A}\bar{B})$$

So after some rearranging we have,

$Pr(AB) = -1 + Pr(\bar{A}\bar{B}) + Pr(B) + Pr(A) = -1 +1.15 = 0.15$.

The points made by others above are completely true, but I think keeping the scope of the problem in mind, you'd be safe to assume that $Pr(A \cup B) = 0.85$.