A fair coin, when tossed, should have an equal chance of landing either side up
In probability theory and statistics, a sequence of independent Bernoulli trials with probability 1/2 of success on each trial is metaphorically called a fair coin. One for which the probability is not 1/2 is called a biased or unfair coin. In theoretical studies, the assumption that a coin is fair is often made by referring to an ideal coin.
John Edmund Kerrich performed experiments in coin flipping and found that a coin made from a wooden disk about the size of a crown and coated on one side with lead landed heads (wooden side up) 679 times out of 1000.[1] In this experiment the coin was tossed by balancing it on the forefinger, flipping it using the thumb so that it spun through the air for about a foot before landing on a flat cloth spread over a table. Edwin Thompson Jaynes claimed that when a coin is caught in the hand, instead of being allowed to bounce, the physical bias in the coin is insignificant compared to the method of the toss, where with sufficient practice a coin can be made to land heads 100% of the time.[2] Exploring the problem of checking whether a coin is fair is a well-established pedagogical tool in teaching statistics.
^Kerrich, John Edmund (1946). An experimental introduction to the theory of probability. E. Munksgaard.
^Jaynes, E.T. (2003). Probability Theory: The Logic of Science. Cambridge, UK: Cambridge University Press. p. 318. ISBN 9780521592710. Archived from the original on 2002-02-05. anyone familiar with the law of conservation of angular momentum can, after some practice, cheat at the usual coin-toss game and call his shots with 100 per cent accuracy. You can obtain any frequency of heads you want; and the bias of the coin has no influence at all on the results!{{cite book}}: CS1 maint: bot: original URL status unknown (link)
a faircoin. One for which the probability is not 1/2 is called a biased or unfair coin. In theoretical studies, the assumption that a coin is fair is...
In statistics, the question of checking whether a coin is fair is one whose importance lies, firstly, in providing a simple problem on which to illustrate...
Coin flipping, coin tossing, or heads or tails is the practice of throwing a coin in the air and checking which side is showing when it lands, in order...
Consider the Bernoulli trial of tossing a faircoin X {\displaystyle X} . The probabilities of the events of the coin landing as heads H {\displaystyle {\text{H}}}...
For example, the information encoded in one "fair" coin flip is log2(2/1) = 1 bit, and in two faircoin flips is log2(4/1) = 2 bits. A 2011 Science article...
10 flips of faircoin = 0.00098 Probability of 1 heads in 10 flips of faircoin = 0.00977 Probability of 2 heads in 10 flips of faircoin = 0.04395 Probability...
her forget that awakening. A faircoin will be tossed to determine which experimental procedure to undertake: If the coin comes up heads, Sleeping Beauty...
include: Flipping a coin. In this context, obverse ("heads") conventionally denotes success and reverse ("tails") denotes failure. A faircoin has the probability...
of whether a tossed coin is fair (i.e. that on average it lands heads up 50% of the time) and an experiment where you toss the coin 5 times. A possible...
coin lands heads up ("H") when tossed. p H {\displaystyle p_{\text{H}}} can take on any value within the range 0.0 to 1.0. For a perfectly faircoin,...
media related to Obverses. Coin collecting Coin flipping Coin orientation Faircoin Medallic orientation List of people on coins Recto and verso of paper...
outcome of a random process. For example, identifying the outcome of a faircoin flip (with two equally likely outcomes) provides less information (lower...
expected value based on population statistics. For example, suppose a faircoin is flipped 100 times. Using the law of averages, one might predict that...
distribution is tossing a coin. Suppose that S {\displaystyle S} is the sample space of all outcomes of a single toss of a faircoin, and X {\displaystyle...
probability spaces. If the experiment consists of just one flip of a faircoin, then the outcome is either heads or tails: Ω = { H , T } {\displaystyle...
response should be thought of as depending on the flip of a faircoin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely....
illustrated as follows. A marker is placed at zero on the number line, and a faircoin is flipped. If it lands on heads, the marker is moved one unit to the...
eventually come to have the same temperature throughout, or that flips of a faircoin may come up heads and tails half the time. A stronger concept than ergodicity...
Coin grading is the process of determining the grade or condition of a coin, one of the key factors in determining its collectible value. A coin's grade...
excluded middle (CEM). Example: (1) If the faircoin had been flipped, it would have landed heads. (2) If the faircoin had been flipped, it would have landed...
{\textstyle p={\frac {1}{2}},} which is for example used to model a faircoin flip. Most important classes of measure spaces are defined by the properties...
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