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At least one of them is a boy. What is the probability that both children are boys? Gardner initially gave the answers 1 / 2 and 1 / 3 , respectively, but later acknowledged that the second question was ambiguous. [1] Its answer could be 1 / 2 , depending on the procedure by which the information "at least one of them is a ...
The computed probability of at least two people sharing the same birthday versus the number of people. In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share the same birthday.
But if instead of an infinite number of flips, flipping stops after some finite time, say 1,000,000 flips, then the probability of getting an all-heads sequence, ,,, would no longer be 0, while the probability of getting at least one tails, ,,, would no longer be 1 (i.e., the event is no longer almost sure).
In the simplest case, if one allocates balls into bins (with =) sequentially one by one, and for each ball one chooses random bins at each step and then allocates the ball into the least loaded of the selected bins (ties broken arbitrarily), then with high probability the maximum load is: [8]
The probability that at least one of the events will occur is equal to one. [4] For example, there are theoretically only two possibilities for flipping a coin. Flipping a head and flipping a tail are collectively exhaustive events, and there is a probability of one of flipping either a head or a tail.
In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events. This inequality provides an upper bound on the probability of occurrence of at least one ...
The conditional probability at any interior node is the average of the conditional probabilities of its children. The latter property is important because it implies that any interior node whose conditional probability is less than 1 has at least one child whose conditional probability is less than 1.
The standard probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. [1] These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases. [2] There are several other (equivalent) approaches to formalising ...