There are 1002 banana-flavored candies and 1002 apple-flavored candies in a box. Lara takes, without looking at the flavor, two candies from the box. If $q$ is the probability that the two candies are of different flavors and $p$ is the probability that the two candies are of the same flavor, what is the value of $q-p$?
(a) 0
(b) $\frac{1}{2004}$
(c) $\frac{1}{2003}$
(d) $\frac{2}{2003}$
(e) $\frac{1}{1001}$
The correct option is (c).

The first candy can be of any flavor. To fix ideas, let's assume it is banana. After this candy is removed, there remain $1002+1001$ candies in the box, in our case, 1002 of apple and 1001 of banana. The probability $q$ that the second candy is different (in our example, apple) is $q=1002 / 2003$. The probability $p$ that the second candy is the same (in our example, banana) is $p=1001 / 2003$. The difference $q-p$ is, therefore,

$$
q-p=\frac{1002}{2003}-\frac{1001}{2003}=\frac{1}{2003}
$$