Re: amarillo slim\'s favorite bet
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In the august 2005 article of cardplayer magazine, there is an interview with evel knievel. In this interview he states that " one of slims favorite tricks was to bet that two of any 25 people chosen at random would have the same birthday. he always won that bet because the math was rediculously in his favor". can anyone here figure the exact odds on this bet? thanks.
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Ignoring Feb. 29th, the probability of a match is:
1 - P(365,25)/365^25 =~ 56.9%
where P(365,25) = 365*364*363*...*341 (25 terms) = 365!/(365-25)!.
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Here is the adjustment for Feb. 29th, which makes the answer closer to 56.8%:
P(match) = 1 - P(no match) =
1 - [ P(no Feb 29th)*P(no match given no Feb 29th) +
P(1 Feb 29th)*P(no match given 1 Feb 29th) ]
1 - { [1 - 1/(4*365.25)]^25 * P(365,25)/365^25 +
25*1/(4*365.25)*[1 - 1/(4*365.25)]^24 * P(365,24)/365^24 }
=~ 56.8%.
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