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What is the probability of winning the car by switching given the player has picked door 1 and the host has opened door 3? 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 ...
An example of double counting is shown starting with the question: What is the probability of seeing at least one 5 when throwing a pair of dice? An erroneous argument goes as follows: The first die shows a 5 with probability 1/6, and the second die shows a 5 with probability 1/6; therefore, the probability of seeing a 5 on at least one of the ...
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Confusion of the inverse, also called the conditional probability fallacy or the inverse fallacy, is a logical fallacy whereupon a conditional probability is equated with its inverse; that is, given two events A and B, the probability of A happening given that B has happened is assumed to be about the same as the probability of B given A, when there is actually no evidence for this assumption.
In another example of near-total neglect of probability, Rottenstreich and Hsee (2001) found that the typical subject was willing to pay $10 to avoid a 99% chance of a painful electric shock, and $7 to avoid a 1% chance of the same shock. They suggest that probability is more likely to be neglected when the outcomes are emotion-arousing.
The Boy or Girl paradox surrounds a set of questions in probability theory, which are also known as The Two Child Problem, [1] Mr. Smith's Children [2] and the Mrs. Smith Problem. The initial formulation of the question dates back to at least 1959, when Martin Gardner featured it in his October 1959 "Mathematical Games column" in Scientific ...
Comparing p(n) = probability of a birthday match with q(n) = probability of matching your birthday. In the birthday problem, neither of the two people is chosen in advance. By contrast, the probability q(n) that at least one other person in a room of n other people has the same birthday as a particular person (for example, you) is given by
In fact, the larger the sample size, the smaller the minimum effect needed to produce a statistically significant p-value (see effect size). Issues 1 and 2 can be illustrated by analogy to the Prosecutor's Fallacy in their shared underlying 2×2 contingency table format, where the user's convenient 90° rotation of attention replaces the ...