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If a cheat has altered a coin to prefer one side over another (a biased coin), the coin can still be used for fair results by changing the game slightly. John von Neumann gave the following procedure: [4] Toss the coin twice. If the results match, start over, forgetting both results. If the results differ, use the first result, forgetting the ...
The three-way flip is 75% likely to work each time it is tried (if all coins are heads or all are tails, each of which occur 1/8 of the time due to the chances being 0.5 by 0.5 by 0.5, the flip is repeated until the results differ), and does not require that "heads" or "tails" be called.
(In practice, it would be more appropriate to assume a prior distribution which is much more heavily weighted in the region around 0.5, to reflect our experience with real coins.) The probability of obtaining h heads in N tosses of a coin with a probability of heads equal to r is given by the binomial distribution:
Intuitively, if both coins are tossed the same number of times, we should expect the first coin turns up fewer heads than the second one. More specifically, for any fixed k , the probability that the first coin produces at least k heads should be less than the probability that the second coin produces at least k heads.
Where the money goes. Some well-known fountains can collect thousands of dollars in coins each year. According to an NBC report from 2016, the Trevi Fountain accumulated about $1.5 million in ...
For You: 5 Coins From the 1960s That Are Worth a Lot of Money. 1969-S Lincoln Cent With a Doubled Die Obverse. A lady in Texas found one of these back in 2014. This was surprising because the ...
Player A selects a sequence of heads and tails (of length 3 or larger), and shows this sequence to player B. Player B then selects another sequence of heads and tails of the same length. Subsequently, a fair coin is tossed until either player A's or player B's sequence appears as a consecutive subsequence of the coin toss outcomes. The player ...
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