Explanation

There are only a couple possible products of these numbers. Indeed, we get a 0 if any of them are 0. We get a 1 if they are all 1's, and also if they are 1's and -1's such that the -1's are even in number. Finally, we can get a -1, the least possible, if we have an odd number of -1's and the rest of the factors 1's. So there are two ways to get a -1: with one -1 and three 1's. and with three -1's and one 1.

Let's start by finding the probability of getting one -1 and three 1's. There are four ways to do this: the negative one is first, second, third, or fourth. The probability of any one specific draw is . Since there are four independent probabilities, we add them to get the odds of obtaining any one of them, so the odds are of one -1 and three 1's. The logic is identical to draw one positive 1 and three negative 1's, so that case also obtains with probability . The probability of obtaining one or the other of these two exclusive cases is their sum (in probability "or" usually means "add"): so are the odds that our product will be -1, the least possible value.

The correct answer is (C).