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Stochastic Processes A group of 5 friends are trying to decide who to vote for in...

Stochastic Processes A group of 5 friends are trying to decide who to vote for in an election: Candidate I or Candidate II. They’re all having a hard time deciding and frequently change their minds. Each morning, exactly one of the friends (chosen at random) updates their preference by flipping a fair coin to decide which candidate to support.

1. Right now, all of the friends support Candidate I. What is the probability that at least one friend will support Candidate II in a week?

2. What is the expected number of days until all of the friends support Candidate I once again?

3. What is the long-term probability that they will unanimously support one candidate?

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