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This can be represented mathematically as follows: If a random experiment can result in N mutually exclusive and equally likely outcomes and if N A of these outcomes result in the occurrence of the event A, the probability of A is defined by =. There are two clear limitations to the classical definition. [18]
For example, when tossing an ordinary coin, one typically assumes that the outcomes "head" and "tail" are equally likely to occur. An implicit assumption that all outcomes are equally likely underpins most randomization tools used in common games of chance (e.g. rolling dice, shuffling cards, spinning tops or wheels, drawing lots, etc.).
When flipping a fair coin 21 times, the outcome is equally likely to be 21 heads as 20 heads and then 1 tail. These two outcomes are equally as likely as any of the other combinations that can be obtained from 21 flips of a coin. All of the 21-flip combinations will have probabilities equal to 0.5 21, or 1 in 2,097,152. Assuming that a change ...
If the results that actually occur fall in a given event, the event is said to have occurred. A probability is a way of assigning every event a value between zero and one, with the requirement that the event made up of all possible results (in our example, the event {1,2,3,4,5,6}) is assigned a value of one. To qualify as a probability, the ...
However, the conclusion that the sun is equally likely to rise as it is to not rise is only absurd when additional information is known, such as the laws of gravity and the sun's history. Similar applications of the concept are effectively instances of circular reasoning , with "equally likely" events being assigned equal probabilities, which ...
This is true even if the die is biased so that 6 and 'not 6' are equally likely to occur (equiprobability). The Principle of Indifference of Laplace states that equipossible alternatives may be accorded equal probabilities if nothing more is known about the underlying probability distribution. However, it is a matter of contention whether the ...
For example, if two fair six-sided dice are thrown to generate two uniformly distributed integers, and , each in the range from 1 to 6, inclusive, the 36 possible ordered pairs of outcomes (,) constitute a sample space of equally likely events. In this case, the above formula applies, such as calculating the probability of a particular sum of ...
In probability theory, an event is a subset of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. [1] A single outcome may be an element of many different events, [2] and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. [3]