A fair coin is flipped 3 times. What is the number of sequences with exactly two heads?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

A fair coin is flipped 3 times. What is the number of sequences with exactly two heads?

Explanation:
To have exactly two heads in three flips, you just choose which one of the three positions will be the tail. There are three possibilities, giving the sequences HHT, HTH, and THH. This matches the count 3 choose 2 = 3. If you needed the probability, each sequence has probability (1/2)^3 = 1/8, so the total probability would be 3/8.

To have exactly two heads in three flips, you just choose which one of the three positions will be the tail. There are three possibilities, giving the sequences HHT, HTH, and THH. This matches the count 3 choose 2 = 3.

If you needed the probability, each sequence has probability (1/2)^3 = 1/8, so the total probability would be 3/8.

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