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This is the birthday paradox problem.
- Avin April 23, 2010In probability theory, birthday paradox pertains to the probability that in a set of randomly chosen people some pair of them will have the same birthday. In a group of at least 23 randomly chosen people, there is more than 50% probability that some pair of them will have the same birthday. Such a result is counter-intuitive to many.
For 57 or more people, the probability is more than 99%,
Thus for a group of 57 we can hope to find a pair of people to have the same birthdays.
As oa said above
let's say # of people with same birthday = B then
B x 1 > (9 - B) x 2 => B > 6. So we need to find at least 7 people that has the same birthday with you to profit.
It is highly unlikely that you find 7 people with the same birthday out of 10. No fool would take the bet. :):):)