Again from Princeton Review's fourth edition, chapter 7 review:

#38 Let X be a random variable on (positive integers) whose distribution function is . Suppose that Y is another random variable whose distribution function is . What is the probability that at least one of the variables X and Y is greater than 2?

(a) 5/6

(b) 64/81

(c) 1/2

(d) 17/81

(e) 1/6

First off, the question seems poorly worded since I am not sure if Y is also a random variable on the positive integers. Furthermore, shouldn't their distribution functions be increasing? The answer in the book is (e). The explanation of the answer seems to treat the functions and as though they are describing the probability that and instead of, what I thought probability distribution functions described, and . Here is the explanation:

The problem asks for the probability that at least one of the variables is greater than 2. That's the same as 1 minus the probability that both variables are less than or equal to 2. Since X and Y are independent, we can multiply the complements of their individual probabilities. So

I understand the logic of the first part, but why is it that they seem to say that ? It seems to me that it would just be , but then again those probability distribution functions don't make sense since they are decreasing...