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Flip a coin until you repeat either heads or tails 2020 times. We will derive the probability that the first coin is the same as

Flip a coin until you repeat either heads or tails 2020 times. We will derive the probability that the first coin is the same as the last coin in the entire sequence of flips.

a) If the process stops after 2021 tosses, what is the probability that the first and last coin are the same?

b) What is the probability that the first coin is the same as the last coin in the entire sequence of flips?

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