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The birthday problem can be generalized as follows: Given n random integers drawn from a discrete uniform distribution with range [1,d], what is the probability p(n; d) that at least two numbers are the same? (d = 365 gives the usual birthday problem.) [15] The generic results can be derived using the same arguments given above.
Carpenter's rule problem; Cauchy problem; Cheryl's Birthday; Circulation problem; Class number problem; Clock angle problem; Common fixed point problem; Congruence lattice problem; Cramer–Castillon problem
A naive application of the even-odd rule gives (,) = = () ()where P(m,n) is the probability of m people having all of n possible birthdays. At least for P(4,7) this formula gives the same answer as above, 525/1024 = 8400/16384, so I'm fairly confident it's right.
Cheryl's Birthday" is a logic puzzle, specifically a knowledge puzzle. [ 1 ] [ 2 ] The objective is to determine the birthday of a girl named Cheryl using a handful of clues given to her friends Albert and Bernard.
An example is the birthday problem, which shows that the probability of two persons having the same birthday already exceeds 50% in a group of only 23 persons. [4] Generalizations of the birthday problem are a key tool used for mathematically modelling coincidences.
A study using the populations of Denmark and Austria (a total of 2,052,680 deaths over the time period) found that although people's life span tended to correlate with their month of birth, there was no consistent birthday effect, and people born in autumn or winter were more likely to die in the months further from their birthday. [8]
Birthday cakes are very commonplace in birthday celebrations. Here, a Black Forest cake is adorned with candles and a topper indicating the recipient's 40th birthday.. A birthday is the anniversary of the birth of a person, or figuratively of an institution.
English: In probability theory, the 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 366 possible birthdays, including February 29).