A fair coin is flipped twice. What is the probability of at least one head?

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Multiple Choice

A fair coin is flipped twice. What is the probability of at least one head?

Explanation:
When flipping a fair coin twice, there are four equally likely outcomes: TT, TH, HT, and HH. At least one head happens in three of these outcomes (TH, HT, HH), so the probability is 3 out of 4, or 3/4. You can see this also by the complement: the only way to have no heads is both tails, which has probability (1/2)×(1/2) = 1/4. Subtract from 1 to get 1 − 1/4 = 3/4. The other options don’t fit because 1/4 corresponds to no heads, 1/2 would miss one of the two favorable patterns, and 1 would assume at least one head is guaranteed.

When flipping a fair coin twice, there are four equally likely outcomes: TT, TH, HT, and HH. At least one head happens in three of these outcomes (TH, HT, HH), so the probability is 3 out of 4, or 3/4. You can see this also by the complement: the only way to have no heads is both tails, which has probability (1/2)×(1/2) = 1/4. Subtract from 1 to get 1 − 1/4 = 3/4. The other options don’t fit because 1/4 corresponds to no heads, 1/2 would miss one of the two favorable patterns, and 1 would assume at least one head is guaranteed.

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