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This article describes experimental procedures for determining whether a coin is fair or unfair. There are many statistical methods for analyzing such an experimental procedure. This article illustrates two of them. Both methods prescribe an experiment (or trial) in which the coin is tossed many times and the result of each toss is recorded.
"Circulating Coins Production data". United States Mint. Archived from the original on March 14, 2016. United States Mint. Archived 2017-01-31 at the Wayback Machine; Archived 2007-03-14 at the Wayback Machine dead links "50 STATE QUARTERS". COINSHEET. Archived from the original on October 27, 2007. "Pennies Minted by the U.S. Mint from 1970 to ...
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.
As visitors' coins splash into Rome's majestic Trevi Fountain carrying wishes for love, good health or a return to the Eternal City, they provide practical help to people the tourists will never meet.
According to legend, throwing a coin into the Trevi Fountain ensures that travelers will return to Rome one day. Approximately €3,000 are thrown into the fountain each day. [25] In 2016, an estimated $1.5 million worth of coins were collected from the fountain. [26] These coins are used to fund a charity supermarket in Rome. [25]
Coin values can be modeled by a set of n distinct positive integer values (whole numbers), arranged in increasing order as w 1 through w n.The problem is: given an amount W, also a positive integer, to find a set of non-negative (positive or zero) integers {x 1, x 2, ..., x n}, with each x j representing how often the coin with value w j is used, which minimize the total number of coins f(W)
With only 2 pence and 5 pence coins, one cannot make 3 pence, but one can make any higher integer amount. Frobenius coin problem with 2-pence and 5-pence coins visualised as graphs: Sloping lines denote graphs of 2 x +5 y = n where n is the total in pence, and x and y are the non-negative number of 2p and 5p coins, respectively.
To answer this, one needs to consider what would be the expected payout at each stage: with probability 1 / 2 , the player wins 2 dollars; with probability 1 / 4 the player wins 4 dollars; with probability 1 / 8 the player wins 8 dollars, and so on.