If you flip two fair coins, what is the probability of getting at least one head?

If you flip two fair coins, what is the probability of getting at least one head?

• A. 3/4
• B. 1/4
• C. 1/2
• D. 2/3

Answer: (A)

When you flip two fair coins, there are four equally likely outcomes: both show heads, the first shows heads and the second tails, the first tails and the second heads, or both show tails. “At least one head” includes every outcome except the both-tails case, so three of the four outcomes satisfy it. That gives a probability of 3/4. Another way to see it is by using the complement: the chance of no heads (both tails) is (1/2) × (1/2) = 1/4. Therefore, 1 − 1/4 = 3/4.

When you flip two fair coins, there are four equally likely outcomes: both show heads, the first shows heads and the second tails, the first tails and the second heads, or both show tails. “At least one head” includes every outcome except the both-tails case, so three of the four outcomes satisfy it. That gives a probability of 3/4.

Another way to see it is by using the complement: the chance of no heads (both tails) is (1/2) × (1/2) = 1/4. Therefore, 1 − 1/4 = 3/4.