| 释义 |
event A (measurable) 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 Ω = {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 A ∩ B of two events is the event that can be described by saying that ‘both A and B occur'. The union A ∪ B of two events is the event that ‘either A or B occurs'. 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(A ∩ B). (ii) When A and B are mutually exclusive events, Pr(A ∪ B) = Pr(A)+Pr(B). (iii) When A and B are independent events, Pr(A ∩ B) = Pr(A) Pr(B). (iv) Pr(A′) = 1 − Pr(A). See probability space. |