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New Problem: One More Coin-Flipping Game

By Mark Eichenlaub

This problem comes from a TED talk by Peter Donnelly

Alice and Bob are flipping fair coins (in a fair manner). They each flip once per second. Alice flips until she gets two consecutive heads, then stops. Bob flips until he gets a heads followed by a tails, then stops.

Who is more likely to stop first? What is Alice’s expected number of tosses before she stops? What is Bob’s? What are the full probability distributions of coin tosses before stopping for Alice and Bob? What is the probability that they tie?

Can you generalize this scenario to longer patterns?

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This entry was posted on July 4, 2009 at 7:48 pm and is filed under problems and solutions. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

One Response to “New Problem: One More Coin-Flipping Game”

  1. Answer: One More Coin-Flipping Game « Arcsecond Says:
    July 14, 2009 at 1:45 am

    [...] Playing on the Sea-Shore, Rough Pebbles Welcome « New Problem: One More Coin-Flipping Game Why Do Taylor Series Converge? (part 1) [...]

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