If a fair coin is flipped #5# times, what is the probability that there will be at least #3# tails?
Here's a quick way to see the answer:
Since the coin is fair, the probability of getting at least three tails must equal the probability of getting at least three heads.
It is easy to see that these two are mutually exclusive (at least three tails means either exactly 3, 4, or 5 tails, while at least three heads means exactly 0, 1, or 2 tails) and exhaust all possibilities. So, the sum of these two probabilities must equal 1 and thus both, being equal, must individually equal