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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 the minimal integer n such that
But given the number of people, what is the probability of every day in the year being someone's birthday? For 1 to 364 people, it is 0, i.e. such a thing is impossible. For exactly 365 people, it is 1/(365!), i.e. 1 divided by the factorial of 365. But what is the probability for larger groups? (For simplicity, we ignore leap years.)
In probability and statistics, an urn problem is an idealized mental exercise in which some objects of real interest (such as atoms, people, cars, etc.) are represented as colored balls in an urn or other container. One pretends to remove one or more balls from the urn; the goal is to determine the probability of drawing one color or another ...
In actuarial science and demography, a life table (also called a mortality table or actuarial table) is a table which shows, for each age, the probability that a person of that age will die before their next birthday ("probability of death"). In other words, it represents the survivorship of people from a certain population. [1]
[6] If the teacher had picked a specific day (say, 16 September), then the chance that at least one student was born on that specific day is (/), about 7.9%. In a birthday attack, the attacker prepares many different variants of benign and malicious contracts, each having a digital signature. A pair of benign and malicious contracts with the ...
This is the same as saying that the probability of event {1,2,3,4,6} is 5/6. This event encompasses the possibility of any number except five being rolled. The mutually exclusive event {5} has a probability of 1/6, and the event {1,2,3,4,5,6} has a probability of 1, that is, absolute certainty.
The classical definition of probability assigns equal probabilities to events based on physical symmetry which is natural for coins, cards and dice. Some mathematicians object that the definition is circular. [11] The probability for a "fair" coin is... A "fair" coin is defined by a probability of... The definition is very limited.
The mathematics of gambling is a collection of probability applications encountered in games of chance and can get included in game theory.From a mathematical point of view, the games of chance are experiments generating various types of aleatory events, and it is possible to calculate by using the properties of probability on a finite space of possibilities.
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