Find the probability that of 25 randomly selected people no 2 share the same birthday? find the following ..?

Question

the probability that at least 2 people sahre the same birthday?

with details and resons please

Answer 1

The infamous birthday problem

http://en.wikipedia.org/wiki/Birthday_pa...

Answer 2

Assuming birthdays are completely random (they certainly aren't), you would actually want to use 365.25, as their birthday could be on a leap year (though this is 1/4 or 0.25 as likely as the other days).

           n - 1

(365.25)¹ ⁻ ⁿ ∏ (365.25 - i)

           i = 1

Where n represents the number of people chosen.

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At 23, the value passes 50%, being approximately 49.29% of nobody sharing the same birthday.

At 25, the chance of nobody having sharing the same birthday is about 43.155%. Thus the chance of them sharing the same birthday is :

100% - 43.155% ≈ 56.8%

——————————————————————————————————————

However, you probably want the "simplified" version:

(365)⁻ ⁿ (365)!/(365-n)!

At n=25, you get about 43.13% chance of none having the same birthday.

From this, you have a 100% - 43.13% = 56.87% chance of them sharing the same birthday.