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In the case of flipping a coin, flipping a head and flipping a tail are also mutually exclusive events. Both outcomes cannot occur for a single trial (i.e., when a coin is flipped only once). The probability of flipping a head and the probability of flipping a tail can be added to yield a probability of 1: 1/2 + 1/2 =1. [5]
The events 1 and 6 are mutually exclusive but not collectively exhaustive. The events "even" (2,4 or 6) and "not-6" (1,2,3,4, or 5) are also collectively exhaustive but not mutually exclusive. In some forms of mutual exclusion only one event can ever occur, whether collectively exhaustive or not.
The probability measure function must satisfy two simple requirements: First, the probability of a countable union of mutually exclusive events must be equal to the countable sum of the probabilities of each of these events. For example, the probability of the union of the mutually exclusive events and in the random experiment of one coin toss ...
In probability theory, the craps principle is a theorem about event probabilities under repeated iid trials. Let E 1 {\displaystyle E_{1}} and E 2 {\displaystyle E_{2}} denote two mutually exclusive events which might occur on a given trial.
The law of total probability is [1] a theorem that states, in its discrete case, if {: =,,, …} is a finite or countably infinite set of mutually exclusive and collectively exhaustive events, then for any event () = ()
To qualify as a probability, the assignment of values must satisfy the requirement that for any collection of mutually exclusive events (events with no common results, such as the events {1,6}, {3}, and {2,4}), the probability that at least one of the events will occur is given by the sum of the probabilities of all the individual events. [28]
This is the same as saying that the probability of event {1,2,3,4,6} is 5/6. This event encompasses the possibility of any number except five being rolled. The mutually exclusive event {5} has a probability of 1/6, and the event {1,2,3,4,5,6} has a probability of 1, that is, absolute certainty.
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.