To determine the probability of getting at least one tail when flipping a fair coin 10 times, we can use the concept of complementary probability. Instead of directly calculating the probability of getting at least one tail, it’s often easier to calculate the probability of the opposite event: getting no tails at all, which means getting all heads.
A fair coin has two possible outcomes: heads (H) and tails (T). The probability of getting heads (P(H)) on a single flip of a fair coin is 0.5, and the same applies to tails (P(T)). Therefore, the probability of flipping 10 heads in a row (which gives us zero tails) can be calculated as:
P(All Heads) = P(H) ^ 10 = (0.5) ^ 10 = 0.0009765625
Now, to find the probability of getting at least one tail, we can subtract the probability of getting all heads from 1:
P(At least one tail) = 1 – P(All Heads) = 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 99.90%.
In conclusion, you have an extremely high probability of getting at least one tail during 10 flips of a fair coin!