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(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%)
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.
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.
For example, if x represents a sequence of coin flips, then the associated Bernoulli sequence is the list of natural numbers or time-points for which the coin toss outcome is heads. So defined, a Bernoulli sequence Z x {\displaystyle \mathbb {Z} ^{x}} is also a random subset of the index set, the natural numbers N {\displaystyle \mathbb {N} } .
The parameter is the probability that a coin lands heads up ("H") when tossed. can take on any value within the range 0.0 to 1.0. For a perfectly fair coin, =. Imagine flipping a fair coin twice, and observing two heads in two tosses ("HH"). Assuming that each successive coin flip is i.i.d., then the probability of observing HH is (=) = =
Most human experience of coin is that they are mostly unbias (even before any coin tosing is performed). So after tossing the coin 10 times with 7 heads and 3 tails. The calculations suggested that the probability that "the toss results came from an unbias coin" is 13% and that the probability that "the toss results came from a bias coin" is 87%.
Probability is the branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [note 1] [1] [2] A simple example is the tossing of a fair (unbiased) coin. Since the ...
Feller's coin-tossing constants are a set of numerical constants which describe asymptotic probabilities that in n independent tosses of a fair coin, no run of k consecutive heads (or, equally, tails) appears. William Feller showed [1] that if this probability is written as p(n,k) then