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(Note: r is the probability of obtaining heads when tossing the same coin once.) Plot of the probability density f(r | H = 7, T = 3) = 1320 r 7 (1 − r) 3 with r ranging from 0 to 1. The probability for an unbiased coin (defined for this purpose as one whose probability of coming down heads is somewhere between 45% and 55%)
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.
Coin grading [1] 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 is generally determined by six criteria: strike, preservation, luster, color, attractiveness, and occasionally the country/state in which it was minted. Several grading systems have been ...
A coin that has not been encapsulated by any coin grading service. [1] reeded edge See milled edge. relief The part of the coin's design that is raised above the field, opposite of incuse. [1] re-strike A coin struck from genuine dies at a date later than the original issue. [1] Some of the 1804 U.S. Silver Dollars were re-strikes. repunched date
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Coin dealers will normally grade these coins at or below the ones shown for that respective type, the grades here depend on how bad the issue or issues are. [27] Grading services typically label these coins as "authentic" with x grade "details" (ex: "EF details"). Coins that are uncirculated as mentioned above can not go below an MS-60 grade.
If a fair coin is flipped 21 times, the probability of 21 heads is 1 in 2,097,152. The probability of flipping a head after having already flipped 20 heads in a row is 1 / 2 . Assuming a fair coin: The probability of 20 heads, then 1 tail is 0.5 20 × 0.5 = 0.5 21; The probability of 20 heads, then 1 head is 0.5 20 × 0.5 = 0.5 21
Tossing coins; Let X n be the fraction of heads after tossing up an unbiased coin n times. Then X 1 has the Bernoulli distribution with expected value μ = 0.5 and variance σ 2 = 0.25. The subsequent random variables X 2, X 3, ... will all be distributed binomially.