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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.
Determining the sex ratio in a large group of an animal species. Provided that a small random sample (i.e. small in comparison with the total population) is taken when performing the random sampling of the population, the analysis is similar to determining the probability of obtaining heads in a coin toss.
A sample space is usually denoted using set notation, and the possible ordered outcomes, or sample points, [5] are listed as elements in the set. It is common to refer to a sample space by the labels S, Ω, or U (for "universal set"). The elements of a sample space may be numbers, words, letters, or symbols.
In the previous example the probability of the set of outcomes ({,}) must be equal to one, because it is entirely certain that the outcome will be either or (the model neglects any other possibility) in a single coin toss. Not every subset of the sample space must necessarily be considered an event: some of the subsets are simply not of ...
Define = {For a fair coin, both realizations are equally likely. We can generate realizations of this random variable X from a U ( 1 , 0 ) {\displaystyle U(1,0)} uniform distribution provided by a random number generator (RNG) by having X = 1 {\displaystyle X=1} if the RNG outputs a value between 0 and 0.5 and X = 0 {\displaystyle X=0} if the ...
[1] [2] It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). [ 3 ] For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads , and ...
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 /
Before the box is selected, there is one sample space consisting of three elements: {box GG, box GS, and box SS}. After a box is selected, there are three sample spaces, each with only one element: {box GG}, {box GS} and {box SS}. The probability for each is simple: divide the number of elements that meet the criterion by the total number of ...