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Alex and Blake each flip a coin until they get their first heads. Given that Alex needed fewer flips than Blake, what is Alex's expected number of flips?

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What is the expected number of fair coin flips needed until the pattern HHT first appears?A coin lands heads with probability 1/4. What is the expected number of flips needed to see three heads?What is the expected number of fair coin tosses to get two heads in a row?

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