To find the probability of getting at least one tail when flipping a fair coin 10 times, it can be easier to first calculate the probability of the opposite event—getting no tails at all (which means getting all heads)—and then subtract that from 1.
1. The probability of getting heads in a single flip of a fair coin is 0.5.
2. The probability of getting heads for all 10 flips is given by:
P(all heads) = (0.5)10 = 0.0009765625
3. Therefore, the probability of getting at least one tail (which is the complement of getting all heads) is calculated as follows:
P(at least one tail) = 1 – P(all heads)
P(at least one tail) = 1 – 0.0009765625 = 0.9990234375
So, the probability of getting at least one tail when flipping a fair coin 10 times is approximately 0.999, or 99.9%.