Same Birthday Math

The birthday paradox is strange counter intuitive and completely true. In a room of 75 there s a 99 9 chance of at least two people matching. 1 the probability that all birthdays of n persons are different.

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A person s birthday is one out of 365 possibilities excluding february 29 birthdays.

Same birthday math. Flip that around and we get the chance of matching. Person a can be born on any day of the year since they re the first person we re asking. The probability of being born any day of. The probability that a person does not have the same birthday as another person is 364 divided by 365 because.

It s only a paradox because our brains can t handle the compounding power of exponents. Calculates a table of the probability that one or more pairs in a group have the same birthday and draws the chart. What is the probability that two people share the same birthday. In a room of just 23 people there s a 50 50 chance of at least two people having the same birthday.

The birthday problem also called the birthday paradox deals with the probability that in a set of n n randomly selected people at least two people share the same birthday. The first person could have any birthday p 365 365 1 and the second person could then have any of the other 364 birthdays p 364 365. In probability theory the birthday problem or birthday paradox concerns the probability that in a set of n randomly chosen people some pair of them will have the same birthday. By the pigeonhole principle the probability reaches 100 when the number of people reaches 367 since there are only 366 possible birthdays including february 29.

11 12 10 12 9 12 8 12 7 12 0 22. These conclusions are based on the assumption that each day. Though it is not technically a paradox it is often referred to as such because the probability is counter intuitively high. So there is a 78 chance of any of them celebrating their birthday in the same month.

Put down the calculator and pitchfork i don t speak heresy. Multiply those two and you have about 0 9973 as the probability that any two people have different birthdays or 1 0 9973 0 0027 as the probability that they have the same birthday. However 99 9 probability is reached with just 70 people and 50 probability with 23 people. So the chance of not matching is.