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In three independent fair coin tosses, what is the probability of exactly one head?

1/8

1/2

3/8

When counting the probability of exactly a certain number of heads in independent fair flips, you multiply the number of ways to place the heads by the probability of any one specific pattern. Here, exactly one head among three flips can occur in three different patterns: H T T, T H T, and T T H. Each specific pattern has probability (1/2)^3 = 1/8. So the total probability is the number of patterns (3) times 1/8, which equals 3/8.

This also lines up with the idea that the binomial probability is C(3,1) (1/2)^3 = 3/8. The other numbers correspond to different events: 1/8 would be just one particular pattern, 1/2 would reflect a single-flip scenario or an average over patterns, and 7/8 is the probability of at least one head (the complement of all tails).

7/8