What is the probability of exactly one head in two flips of a fair coin?

• A. 0
• B. 1/4
• C. 3/4
• D. 1/2

Answer: (D)

Think of two independent flips of a fair coin. There are four equally likely results: heads-heads, heads-tails, tails-heads, and tails-tails. Exactly one head happens in the two mixed results (heads-tails and tails-heads), which gives 2 favorable outcomes out of 4 total. So the probability is 2/4, which equals 1/2.

You can also use the binomial idea: there is 1 choice of which flip shows the single head among the two flips, times the probability (1/2) for that head and (1/2) for the tail, giving 2 × (1/2) × (1/2) = 1/2.

The other numbers don’t fit because 0 would mean no way to get exactly one head, 1/4 would represent only one specific arrangement, and 3/4 would correspond to getting at least one head, not exactly one.