If you flip a coin three times, what's the probability of getting at least one "tail"?

This classic probability puzzle is best solved by looking at it backwards. Instead of counting all the ways to get at least one tail, it's much simpler to figure out the probability of the one outcome you *don't* want: getting no tails at all. The only way for that to happen is to flip three heads in a row (HHH). The probability of getting heads on a single flip is 1/2. To find the probability of it happening three consecutive times, you multiply the odds: 1/2 x 1/2 x 1/2, which equals 1/8.

Since the 1/8 chance of getting all heads is the only scenario that fails the condition, every other possible outcome must contain at least one tail. In probability, the total of all possible outcomes is always 1 (or 100%). By subtracting the single unwanted outcome from the total, you find the probability of what you're looking for. So, 1 minus 1/8 leaves you with the final probability of 7/8.

If you're skeptical, you can list all eight possible combinations from three flips: HHH, HHT, HTH, THH, HTT, THT, TTH, and TTT. A quick count shows that seven of those eight possibilities include a tail, confirming the result. This illustrates a powerful concept known as the complement rule, which is often the easiest way to calculate the probability of "at least one" of something happening.