Mathematical Food for Thought

 
 
 
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    Serves a Daily Special and an All-You-Can-Eat Course in Problem Solving. Courtesy of me, Jeffrey Wang.
 
Something To Think About. Topic: Probability. Level: AMC/AIME. April 18th, 2007

Problem: A coin is repeatedly flipped. What is the expected number of flips to get two heads in a row?  n heads in a row?

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I will be out of town for the next four days, so have fun with the problem!

4 Responses to “Something To Think About. Topic: Probability. Level: AMC/AIME.”

  1. Xuan Says:

    four times for the two heads in a row
    and… 2n for n heads in a row

    wahhhhhhh

    so ur at stanford?? u miss out on concessions… MOOO

  2. paladin8 Says:

    Yeah, I’m at Stanford right now. And both of your answers are wrong =P.

  3. t0rajir0u Says:

    Xuan, those answers are correct for n heads total, but it takes a lot more effort to get them all in a row.

    Anyway, the recursion for n looks really ugly…

  4. 4PV-177945 - Besa Pendant Says:

    Another Day, Another Post

    [...] I highly recommend that you check out this blog, I found it quite fascinating [...]

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