What Is The Birthday Paradox

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The birthday paradox, also known as the birthday problem, states that in a random gathering of 23 people, there is a 50% chance that two people will have the same birthday. Is this really true? With 23 people there’s a 50-50 chance of two people having the same birthday. In a room of 75 there’s a 99.9% chance of two people matching. “Birthday paradox is strange, counter-intuitive, and completely true. It’s only a “paradox because our brains can’t handle the compounding power of exponents.” How is this possible? The math behind the birthday paradox has to do with probability. It is important to take in consideration, that in order to find out the probability of people who has the same birthday, what is the probability that they
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P(s) + P(d) = 1 or 100%, therefore, P(s) = 100% - P(d). We know there are 365 days in a year, out of all those days what is the probability that 2 people have the same birthday. For every person in the group you subtract the number of days in the year. For example, if there are 30 people you would subtract 30 from 365 and that would give you 335. Then you would subtract divide (365!/335!)/(365)^30, that would give you .2937 which you then would convert into percentage 29.37%. So 29.37% is the percentage and probability that people have different birthdays out of the 30. We are trying to find out what the probability is for people who have the same birthday. In order to determine that you would take the formula given above and then plug the numbers in. P(s)=100%-29.37%. You would then end up with P(s)…show more content…
Therefore, the probability he would fin is 2/529. This, however, differentiates from the original way of solving because in order to find the probability you would divide the number of days in a year ! (365!) over the number of days in a year minus the number of people in the room, 365!/342! Divided by (365)^23 would give you .491266 which is equivalent to 49%. After that you would subtract the percent given (49.12%) from 100% which would give you 50.88%. The difference in how that was figured out was that there is a formula that makes things more useful. Another method that was considered when trying to find the answer to the “Birthday Paradox”, was pairing up the number of people with the number of days. For example, on examination can be trying to find the 1 out of the 10 people that shares a birthday with someone else out of 4 days in a year.So you would write it out so that it looks as if they are pairing
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