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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.
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.
This leads to different choices of sample space. The σ-algebra is a collection of all the events we would like to consider. This collection may or may not include each of the elementary events. Here, an "event" is a set of zero or more outcomes; that is, a subset of the sample space. An event is considered to have "happened" during an ...
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 random experiment is described or modeled by a mathematical construct known as a probability space. A probability space is constructed and defined with a specific kind of experiment or trial in mind. A mathematical description of an experiment consists of three parts: A sample space, Ω (or S), which is the set of all possible outcomes.
The game host then opens one of the other doors, say 3, to reveal a goat and offers to let the player switch from door 1 to door 2. The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal and named after its original host, Monty Hall.
That is, the probability function f(x) lies between zero and one for every value of x in the sample space Ω, and the sum of f(x) over all values x in the sample space Ω is equal to 1. An event is defined as any subset E {\displaystyle E\,} of the sample space Ω {\displaystyle \Omega \,} .
In probability theory, a tree diagram may be used to represent a probability space. A tree diagram may represent a series of independent events (such as a set of coin flips) or conditional probabilities (such as drawing cards from a deck, without replacing the cards). [ 1 ]