The best way to determine the probability of at least one success is to find the probability of having no successes and subtracting it from 1. We'll apply the same principle to both questions.
If the movies are selected with replacement, then we consider the events to be independent. It's like the probability hits the "reset button." The probability of neither movie selected being a drama is the product of the probabilities of two selections that are not dramas. The probability of selecting 1 non- drama is 3/7. The probability of selecting 2 non-dramas is 3/7 · 3/7 = 9/49. So the probability of this not happening, which is the probability of choosing at least 1 drama, is 1 - 9/49 = 40/49.
If the movies are selected without replacement, then they are not independent. The best way I can think to do this one is by using combinations. We'll use the same principle of finding the probability of its opposite (complement). How many ways can one choose a 2 movies out of 7, without replacement? The answer is 7C2 = 21. In how many of those ways are neither of them dramas? From a combination perspective, this means choosing two movies from the non-dramas, which is 3C2 = 3. So the probability that neither movie is a drama is 3/21, or 1/7. So the probability this doesn't happen, which is the probability that at least one is a drama, is 1 - 1/7 = 6/7.
