The probability of a fair coin resulting in no heads after three flips is 0.5 multiplied by itself three times, which equals 0.1250 when rounded to four decimal places.
The question asks to find the probability that there are no heads (H) when a fair coin is flipped three times. The sample space for one flip of a fair coin is {H, T}.
To find the probability of no heads in three flips, we need to consider only the case of getting all tails (TTT), since this is the only outcome with no heads at all.
The probability of getting a tail on one flip is 0.5 (since the coin is fair), and since each flip is independent, the probabilities can be multiplied for consecutive events.
Thus, the probability of getting all tails in three flips is:
Probability Calculation
P(TTT) = P(T) x P(T) x P(T)
P(TTT) = 0.5 x 0.5 x 0.5
P(TTT) = 0.125
When rounded to four decimal places, the probability is 0.1250.