Defining Probability von Edu Pristine

Dozent des Vortrages Defining Probability

Edu Pristine

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... Can be defined as the set of all the outcomes of an event, usually denoted by letter S. Examples: In tossing a coin we can get either head or a tail, the sample space S will be denoted by S={H,T}. If we toss a die we can get any number from 1 to 6. The sample space will be denoted by S={1,2,3,4,5,6} ...

... Sample Point: Each of the outcome of any experiment, an element of the sample space. Example: Appearance of head on throwing of a die. Events: Any particular outcome or a combination of outcomes ...

... Since A represents the event for obtaining an even numbers A={2,4,6} where as the total outcomes in tossing a die can be {1,2,3,4,5,6} that is any number can appear on tossing a die. Therefore P(A) = Total number of favorable outcomes (obtaining even numbers). Total number of outcomes on tossing a die = 3/6 = 0.5. The probability of A not occurring is P(not A)=P(A). For instance, the probability of the die showing an odd number is also 0.5 ...

... If A and B be two events occurring with probabilities P(A) and P(B), P(A or B) = P(A)+P(B) P(A and B), where P(A and B) is the probability of occurrence of both events A and B simultaneously mathematically. Example: From a deck of 52 cards a card is drawn, find the probability that a card is a spade or queen. ...

... Example: The event A1: An operation is successful in its first trial. The event A2: An operation is not successful in its first trial. A1 and A2 are mutually exclusive because it is simultaneously not possible that event can be successful and failure at the same time. In the above example ...

... Probability of some event A, given the occurrence of some other event B. Written P(A|B) and is read "the probability of A, given B". Mathematically: P(A|B) = P(A|B)/P(B). Example: Consider the experiment of tossing three fair coins, find the probability that at least two heads appear given that the first coin shows tail. S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Since the coins are fair, the probability of each event is 1/8. ...