035. Relationships between Events

Two events are said to be Mutually exclusive if the occurrence of one event precludes the occurrence of the other: If one vent happens, the other cannot.

An Example Of mutually exclusive events is flipping a head or a tail in a single coin flip. If the head occurs, the tail cannot. Other example is rolling a 3 or even number, drawing from a 52-card deck one card that is a queen or an ace, etc.

Collectively exhaustive events are those events that consist of all possible outcomes of an experiment. In a case of rolling a die, the collectively exhaustive events are 1, 2, 3, 4, 5, and 6. The collectively exhaustive events for an experiment constitute its sample space.

Independent events are events which independent if the occurrence of one event has no effect on the probability that the second will occur. For Example, since the result of drawing a card from a deck has no impact on whether it rains tomorrow, the result of the draw is independent of tomorrow’s weather.

Complementary events are events such that if one does not occur, the other must. The complement of A Is written Ā, and is referred to as “not A”. For Example, if A is rolling an even number with a die (2, 4, or 6), the Complement is rolling an odd number (1, 3, or 5). Complementary events are also collectively exhaustive, because if A does not occur, Ā Must occur. Thus,

P(A) + P(Ā) = 1,

P(A) = 1 – P(Ā).

< Предыдущая		Следующая >