Calculating Real Odds

This is based on a question from Black Swan by Nassim Taleb.

Imagine the following real event:  You are at a vacation resort that will occasionally serve meals with assigned seating where you meet other people at the resort.  You find yourself at dinner with four people you have never met before: Alice, Bob, Carlos, and Darla.  Darla pulls out a coin and says,”I have a 50-50, heads-tails coin, so I thought we’d pass the time by doing some statistics.” She flips the coin and it lands heads.  She flips it again and it lands heads.  She flips it 99 times and it lands heads every time.  “Wow,” she says, “What do you think it will be the 100th time?”

Alice says, “It’s been heads so many times, the odds are overwhelmingly in favor of tails this time.”

Bob says, “The odds are still 50-50, so there is still equal probability of a heads or a tails occurring.”

Carlos says, “It’s been heads so many times, I think it will be heads again.”

With whom do you agree?

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