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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.
(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%)
The probability of getting two heads in two tosses is 1 / 4 (one in four) and the probability of getting three heads in three tosses is 1 / 8 (one in eight). In general, if A i is the event where toss i of a fair coin comes up heads, then:
Coin flipping, coin tossing, or heads or tails is the practice of throwing a coin in the air and checking which side is showing when it lands, in order to randomly choose between two alternatives. It is a form of sortition which inherently has two possible outcomes.
It can be used to represent a (possibly biased) coin toss where 1 and 0 would represent "heads" and "tails", respectively, and p would be the probability of the coin landing on heads (or vice versa where 1 would represent tails and p would be the probability of tails). In particular, unfair coins would have /
A gambler's fortune (capital) is a martingale if all the betting games which the gambler plays are fair. The gambler is playing a game of coin flipping. Suppose X n is the gambler's fortune after n tosses of a fair coin, such that the gambler wins $1 if the coin toss outcome is heads and loses $1 if the coin toss outcome is tails. The gambler's ...
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 ...
Furthermore, the more often the coin is tossed, the more likely it should be that the ratio of the number of heads to the number of tails will approach unity. Modern probability theory provides a formal version of this intuitive idea, known as the law of large numbers. This law is remarkable because it is not assumed in the foundations of ...