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A rooster starts at the position 2017 on a number line. Every minute, the rooster flips a fair two-sided coin, and moves one step to the right if the coin lands heads, and one step to the left if the coin lands tails. The Wise Rooster Oracle predicts that the rooster will eventually reach position 2500 before reaching position 0. Assuming that this information from the future is accurate, what is the probability that the first coin flip will be heads (so after the first minute, the rooster will move to 2018 rather than 2016)? Write your answer as a fraction p/q in simplest terms.
A rooster starts at the position 2017 on a number line. Every minute, the rooster flips a fair two-sided coin, and moves one step to the right if the coin lands heads, and one step to the left if the coin lands tails. The Wise Rooster Oracle predicts that the rooster will eventually reach position 2500 before reaching position 0. Assuming that this information from the future is accurate, what is the probability that the first coin flip will be heads (so after the first minute, the rooster will move to 2018 rather than 2016)? Write your answer as a fraction p/q in simplest terms.
1 Answer
Explanation:
If the coin is fair, the probability of a "heads" on any single flip is independent of any other factors; that is
