Math Trivia : Same birthday in the class of 50 people

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Bet is made on "Are there the two persons with same birthday in the class of 50 people or not?" 
Should I bet on "Yes" ? 



Yes, you should.

The probability that birthday of two people is not the same, should be subtracted from 1.
Then you can find the probability that there are two persons with same birthday.

 Probability of that birthday of #1 person and #2 person of the attendance numbers is different, is 364/365.
The probability of that #3 person is not the same birthday with both #1 and #2 is 363/365.

 Calculating up to # 50 like this, the probability that there is no person with same birthday among 50 people is to be 364/365 × 363/365 × · · · · · × 316/365 = 0.0296 (Please believe this is correct as the calculation is very tough.).
Therefore, the probability that there are two persons with the same birthday is 1 - 0.0296 = 0.9704 = about 97% and you should bet on "Yes".