Friday, October 1, 2010

PUZZLE: The Blue-Eyed Sisters

Here's another one from Martin Gardner:

If you happen to meet two of the Jones sisters (this assumes that the two are random selections from the set of all the Jones sisters), it is an exactly even-money bet that both girls will be blue-eyed. What is your best guess as to the total number of blue-eyed Jones sisters?
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3 comments:

  1. AnonymousOctober 1, 2010 at 11:06 AM

    Ack! I'm getting something involving the square root of 2. That can't be right...

    ReplyDelete
  2. Joshua FaheyOctober 1, 2010 at 11:21 AM

    3.

    ReplyDelete
  3. Thomas L. McDonaldOctober 1, 2010 at 2:03 PM

    Here's the math: b(b-1)/n(n-1)

    The probability is 1/2, so you need to find integral values for b & n that will yield 1/2.

    The smallest such values are n=4 & b=3. The next highest values are n=21 & b=15, but there's unlikely to be that many sisters.

    So, you have 4 sisters total, 3 of whom are blue-eyed.

    ReplyDelete

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