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# event

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A subset of the sample space relating to an experiment. For example, suppose that the sample space for an experiment in which a coin is tossed three times is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}, and let A={HHH, HHT, HTH, THH}. Then A is the event in which at least two ‘heads’ are obtained. If, when the experiment is performed, the outcome is one that belongs to A, then A is said to have occurred. The intersection AB of two events is the event that can be described by saying that ‘both A and B occur’. The union AB of two events is the event that ‘either A or B occurs’. Taking the sample space as the universal set, the complement A′ of A is the event that ‘A does not occur’. The probability Pr(A) of an event A is often of interest. The following laws hold:(i) Pr(A ∪ B)=Pr(A)+Pr(B)−Pr(AB).(ii) When A and B are mutually exclusive events, Pr(AB)=Pr(A)+Pr(B).(iii) When A and B are independent events, Pr(AB)=Pr(A) Pr(B).(iv) Pr(A′)=1−Pr(A).

(i) Pr(A ∪ B)=Pr(A)+Pr(B)−Pr(AB).

(ii) When A and B are mutually exclusive events, Pr(AB)=Pr(A)+Pr(B).

(iii) When A and B are independent events, Pr(AB)=Pr(A) Pr(B).

(iv) Pr(A′)=1−Pr(A).

Subjects: Mathematics.

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