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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.
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.
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 ...
The probability of 20 heads, then 1 head is 0.5 20 × 0.5 = 0.5 21 The probability of getting 20 heads then 1 tail, and the probability of getting 20 heads then another head are both 1 in 2,097,152. When flipping a fair coin 21 times, the outcome is equally likely to be 21 heads as 20 heads and then 1 tail.
Suppose one wishes to determine just how biased an unfair coin is. Call the probability of tossing a 'head' p. The goal then becomes to determine p. Suppose the coin is tossed 80 times: i.e. the sample might be something like x 1 = H, x 2 = T, ..., x 80 = T, and the count of the number of heads "H" is observed.
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.
To choose two out of three, three coins are flipped, and if two coins come up the same and one different, the different one loses (is out), leaving two players. To choose one out of three, the previous is either reversed (the odd coin out is the winner) or a regular two-way coin flip between the two remaining players can decide. The three-way ...