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The answer to the first question is 2 / 3 , as is shown correctly by the "simple" solutions. But the answer to the second question is now different: the conditional probability the car is behind door 1 or door 2 given the host has opened door 3 (the door on the right) is 1 / 2 .
A veridical paradox is a paradox whose correct solution seems to be counterintuitive. It may seem intuitive that the probability that the remaining coin is gold should be 1 / 2 , but the probability is actually 2 / 3 . [1] Bertrand showed that if 1 / 2 were correct, it would result in a contradiction, so 1 / 2 ...
The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the belief that, if an event (whose occurrences are independent and identically distributed) has occurred less frequently than expected, it is more likely to happen again in the future (or vice versa).
In an alternative formulation of the birthday problem, one asks the average number of people required to find a pair with the same birthday. If we consider the probability function Pr[n people have at least one shared birthday], this average is determining the mean of the distribution, as opposed to the customary formulation, which asks for the ...
Each prisoner has to find their own number in one of 100 drawers, but may open only 50 of the drawers. The 100 prisoners problem is a mathematical problem in probability theory and combinatorics. In this problem, 100 numbered prisoners must find their own numbers in one of 100 drawers in order to survive.
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p).
Brainly is an education company based in Kraków, Poland, with headquarters in New York City.It is an AI-powered homework help platform targeting students and parents. As of November 2020, Brainly reported having 15 million daily active users, making it the world's most popular education app. [2] In 2024, FlexOS reported Brainly as the #1 Generative AI Tool in the education category and the #6 ...
In fact, as ε approaches 0, the total probability goes to 1 / 2 , which is the answer expected when one child is sampled (e.g. the oldest child is a boy) and is thus removed from the pool of possible children. In other words, as more and more details about the boy child are given (for instance: born on January 1), the chance that the ...