We will compute the converse probability, that is the probability that no two people in front of you share the same birthday.
Ok , let us calculate the probability that first two people don't have the same birthday:
(365/365) x (364/365) = 99.72 %
The probability that first three people don't have the same birthday is:
(365/365) x (364/365) x (363/365) = 99.17 %
Ok , let us calculate the probability that first two people don't have the same birthday:
(365/365) x (364/365) = 99.72 %
The probability that first three people don't have the same birthday is:
(365/365) x (364/365) x (363/365) = 99.17 %
The probability that first four people don't have the same birthday is:
(365/365) x (364/365) x (363/365) x (362/365) = 98.36 %
so on...
The probability that first 57 people don't have the same birthday is:
(365/365) x (364/365) x (363/365) x ... x(310/365) x (309/365) = 0.98 % = 1 % (approx)
This means there a 99% chance that at least two people in front of you in the queue have the same birthday.
Here is graph showing the variation of chance of two people having same birthday over the total number of people in front of you .
(365/365) x (364/365) x (363/365) x (362/365) = 98.36 %
so on...
The probability that first 57 people don't have the same birthday is:
(365/365) x (364/365) x (363/365) x ... x(310/365) x (309/365) = 0.98 % = 1 % (approx)
This means there a 99% chance that at least two people in front of you in the queue have the same birthday.
Here is graph showing the variation of chance of two people having same birthday over the total number of people in front of you .
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