WebJan 31, 2012 · Solution to birthday probability problem: If there are n people in a classroom, what is the probability that at least two of them have the same birthday? General solution: P = 1-365!/ (365-n)!/365^n. If you try to solve this with large n (e.g. 30, for which the solution is 29%) with the factorial function like so: P = 1-factorial (365 ... WebThe frequency lambda is the product of the number of pairs times the probability of a match in a pair: (n choose 2)/365. Then the approximate probability that there are exactly M …
The matching, birthday and the strong birthday problem: a …
http://prob140.org/textbook/content/Chapter_01/04_Birthday_Problem.html In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share a birthday. The birthday paradox refers to the counterintuitive fact that only 23 people are needed for that probability to exceed 50%. The birthday paradox is a veridical paradox: it … See more From a permutations perspective, let the event A be the probability of finding a group of 23 people without any repeated birthdays. Where the event B is the probability of finding a group of 23 people with at least two … See more Arbitrary number of days Given a year with d days, the generalized birthday problem asks for the minimal number n(d) such that, in a set of n randomly chosen people, the probability of a birthday coincidence is at least 50%. In other words, n(d) is … See more A related problem is the partition problem, a variant of the knapsack problem from operations research. Some weights are put on a balance scale; each weight is an integer number of … See more The Taylor series expansion of the exponential function (the constant e ≈ 2.718281828) $${\displaystyle e^{x}=1+x+{\frac {x^{2}}{2!}}+\cdots }$$ See more The argument below is adapted from an argument of Paul Halmos. As stated above, the probability that no two birthdays … See more First match A related question is, as people enter a room one at a time, which one is most likely to be the first to have the same birthday as … See more Arthur C. Clarke's novel A Fall of Moondust, published in 1961, contains a section where the main characters, trapped underground for an indefinite amount of time, are … See more how to light up water heater pilot
Birthday Problem – Math Fun Facts - Harvey Mudd College
WebMay 3, 2012 · The problem is to find the probability where exactly 2 people in a room full of 23 people share the same birthday. My argument is that there are 23 choose 2 ways times 1 365 2 for 2 people to share the same birthday. But, we also have to consider the case involving 21 people who don't share the same birthday. This is just 365 permute 21 … WebApr 9, 2012 · The birthday matching problem is a classic problem in probability theory. The part of it that people tend to remember is that in a room of 23 people, there is greater than 50% chance that two people in … WebThe simplest solution is to determine the probability of no matching birthdays and then subtract this probability from 1. Thus, for no matches, the first person may have any of … how to light up the keyboard