So the birthday paradox is where if you’re in a room with 23 other people there’s a 50% chance of at least two people having the same birthday. Alternatively, In a room of 75 there’s a 99.9% chance of at least two people matching.
Why is this?
In: 134
The logic behind the probability of two people sharing a birthday being 1/365 is thus:
Pick a date at random(say March 1). What are the odds that person A birthday is March 1? 1/365. What are the odds of person B having a birthdate of March 1? 1/365. Odds of A and B having birthdate March 1?
P(A and B) = (1/365)* (1/365)
Now the question isnt about a particular date, but rather if they share a birthday regardless of the date. So we need to calculate the probability of not just March 1 but every possible date in the calendar(not assuming leap year), which is 365. So the probability becomes 365 times P(A and B) which is:
= 365* (1/365)* (1/365)
= 1/365.
There you go
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