A fair two-coin flip has what probability of at least one head?

A fair two-coin flip has what probability of at least one head?

• A. 1/4
• B. 1/2
• C. 3/4
• D. 1

Answer: (C)

When you flip two fair coins, think about all the possible results and how many of them include at least one head. The four equally likely outcomes are: heads-heads, heads-tails, tails-heads, and tails-tails. Three of these outcomes have at least one head, so the probability is 3 out of 4, or 3/4. You can also see this with the complement rule: the only way to have no heads is both tails, which is (1/2) × (1/2) = 1/4. Subtracting from 1 gives 1 − 1/4 = 3/4.

When you flip two fair coins, think about all the possible results and how many of them include at least one head. The four equally likely outcomes are: heads-heads, heads-tails, tails-heads, and tails-tails. Three of these outcomes have at least one head, so the probability is 3 out of 4, or 3/4.

You can also see this with the complement rule: the only way to have no heads is both tails, which is (1/2) × (1/2) = 1/4. Subtracting from 1 gives 1 − 1/4 = 3/4.