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# birthday - The Birthday Problem or Paradox Let us assume...

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The Birthday Problem or Paradox Let us assume that a person's birthday falls on any day of the year with equal probability (chance). In other words, there is no inherent bias for one day versus another. (In practice may not be strictly true, but close enough.) Now suppose random 10 people assemble in a room. How likely is it that two of them have the same birthday? What is the likelihood if 25 people assemble? How many people are needed to have a 50% chance of "two people with the same birthday"? It's called the Birthday Problem, and sometimes Birthday Paradox because the answer is counter-intuitive. One may think that for 50% probability, may be 365/2 = 182 people are needed, but in fact only 23 suffice!!! Let's start with the basics. Suppose two random people in the room; what is the probability that they have the same birthday? Prob[2 people with same birthday] = 1/365 (the second person has to have the same birthday as the first one, and since all birthdays are equally likely, this happens with prob 1 in 365] Now suppose there are some k people in the room, and we want to calculate the prob that

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