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Matthew Leingang

Some Really Hard Probability Problems - 0 views

ocw.mit.edu/...prob.pdf

shared by Matthew Leingang on 21 Jul 09 - No Cached
  • Marc Tourangeau on 21 Jul 09
     
    I pulled this up from the MIT Open CourseWare page under their Problem Solving class. I think they use problems of this caliber to prepare for the Putnam exam.
  • ...2 more comments...
  • Sam V on 21 Jul 09
     
    I wonder if we as a class could take on this one... 3. An unfair coin (probability p of showing heads) is tossed n times. What is the probability that the number of heads will be even?
  • Matthew Leingang on 21 Jul 09
     
    That's a great idea. First, try it for specific values of n. If n=1, then the number of heads is even if it's 0, so P(even) = 1-p. If n=2, you could have 0 or 2 heads, so P(even) = (1-p)^2 +p^2 = 1-2p. Obviously there's going to be some kind of binomial identity, but what?
  • Matthew Leingang on 22 Jul 09
     
    OK, I now know two ways to solve this. The first way was along the lines you described in the break to me, Sam. It makes more sense than I originally thought, and with your Discrete Math knowhow you might be able to solve it. There's also a clever way, which I admit I didn't figure out until I solved it the other way.
  • Matthew Leingang on 22 Jul 09
     
    That's a great list of problems btw!
Sam V

The Probability Web: Quotations - 0 views

www.mathcs.carleton.edu/...quotes.html

math probability thoughts philosophy quotations v63.0233.2009su

shared by Sam V on 06 Aug 09 - Cached
  • Sam V on 06 Aug 09
     
    A collection of notable quotes regarding probability.
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