Conditional probability:
The probability of occurrence of the event B when it is known that some of the event A has occurred is called as condition probability and can be denoted by P(B/A). The symbol P(B/A) is read probability that B occurs given that A occurs or simply probability of B, given A.
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Consider 2 events 'A' and 'B' of sample-space S. When it is known that event A has happened already, it means that sample space would reduce to sample points representing event A. Now for P(B/A) we should look for sample points representing he simultaneous occurrence of A and B that is sample points in A∩B.
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Consider event 'B' of getting a '4' when the fair die is tossed. Now assume that it is known that toss of die resulted in the number greater than 3. And we have to obtain P(B/A)
That is the probability of getting a '4' given that a number is greater than 3 has occurred. Obviously
Example: The probability that married man watches a certain T.V. show is 0.4 and the probability that married woman watches the show is 0.5. The probability that man watches the show, given that wife does, is 0.7. Find out
(a) the probability that the married couple watch the show
(b) the probability that the wife watches the show given that her husband does.
(c) the probability that atleast 1 person of a married couple will watch the show.
Sol: Let 'H' be event that the married man watches show and 'W' be probability that married woman watch show,
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