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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.
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.
"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 ...
Any $2 bill printed after 1976 won’t be worth more than $2, even in excellent condition. However, $2 bills printed between 1862 and 1918 can be worth $50 in well-circulated condition and $500 or ...
1) Subdivide the coins in to 2 groups of 4 coins and a third group with the remaining 5 coins. 2) Test 1, Test the 2 groups of 4 coins against each other: a. If the coins balance, the odd coin is in the population of 5 and proceed to test 2a. b. The odd coin is among the population of 8 coins, proceed in the same way as in the 12 coins problem.
This is not the case for arbitrary coin systems or even some real world systems, though. For instance, if we consider the old (now withdrawn) Indian coin denominations of 5, 10, 20 and 25 paise, then to make 40 paise, the greedy algorithm would choose three coins (25, 10, 5) whereas the optimal solution is two coins (20, 20).
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.
The first time heads appears, the game ends and the player wins whatever is the current stake. Thus the player wins 2 dollars if heads appears on the first toss, 4 dollars if tails appears on the first toss and heads on the second, 8 dollars if tails appears on the first two tosses and heads on the third, and so on.