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GRE · Question of the Day

GRE Question of the Day

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Friday, August 7, 2026

A fair coin is flipped 3 times. The sample space consists of all sequences of length 3 made of H and T, with each of the 8 sequences equally likely. What is the probability of getting at least one head?

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Question of the Day

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A fair coin is flipped 3 times. The sample space consists of all sequences of length 3 made of H and T, with each of the 8 sequences equally likely. What is the probability of getting at least one head?

  1. 18\frac{1}{8}
  2. 38\frac{3}{8}
  3. 78\frac{7}{8} (correct answer)
  4. 12\frac{1}{2}
  5. 58\frac{5}{8}

Explanation: This question tests probability of complementary events in repeated independent trials. The sample space consists of 8 equally likely sequences of H and T from 3 coin flips. The probability of all tails is 1/8, so the probability of at least one head is 1 - 1/8 = 7/8. Counting directly, there are 7 sequences with at least one H. This result is justified because the complement (all tails) is a single outcome, making the calculation straightforward and efficient for 'at least' problems. A tempting incorrect option is 3/8, perhaps from confusing it with exactly one head (which has 3 outcomes). This fails because 'at least one' includes exactly one, two, and three heads, not just one.