When a fair coin is flipped twice, what is the probability of at least one head?

• A. 1/4
• B. 3/4
• C. 1
• D. 1/2

Answer: (B)

When you want the chance of at least one head in two flips, consider the opposite event: no heads at all, which means tails on both flips. The probability of tails on each flip is 1/2, so tails-tails has probability (1/2) × (1/2) = 1/4. Therefore, the probability of at least one head is 1 − 1/4 = 3/4.

You can also see this by listing all outcomes: HH, HT, TH, TT. The first three have at least one head, so 3 out of 4 possible outcomes work, giving 3/4.

Why the other numbers don’t fit: 1/4 is the chance of getting no heads (TT). 1 would mean at least one head is guaranteed, which isn’t the case here. 1/2 matches the probability of getting exactly one head in two flips, not at least one head.