Two fair coins are flipped. What is P(at least one head)?

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Multiple Choice

Two fair coins are flipped. What is P(at least one head)?

When two fair coins are flipped, each flip has two equally likely outcomes, and the flips are independent, so there are four equally likely result pairs: heads-heads, heads-tails, tails-heads, and tails-tails. The event “at least one head” occurs in the first three pairs, but not in tails-tails. That’s 3 favorable outcomes out of 4 total, giving a probability of 3/4, which is 0.75. Another way to see it is the complement: the only way to have no heads is tails-tail, which has probability 1/4, so at least one head is 1 − 1/4 = 3/4 = 0.75.

When two fair coins are flipped, each flip has two equally likely outcomes, and the flips are independent, so there are four equally likely result pairs: heads-heads, heads-tails, tails-heads, and tails-tails. The event “at least one head” occurs in the first three pairs, but not in tails-tails. That’s 3 favorable outcomes out of 4 total, giving a probability of 3/4, which is 0.75. Another way to see it is the complement: the only way to have no heads is tails-tail, which has probability 1/4, so at least one head is 1 − 1/4 = 3/4 = 0.75.

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