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?
Friday, October 1, 2010
PUZZLE: The Blue-Eyed Sisters
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:
Ack! I'm getting something involving the square root of 2. That can't be right...
3.
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.
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