if A and B are two independent events,then the probability of occourrence at least one of A and Bis given by 1-p(A')p(B')

Asked by neesa.vs | 15th Mar, 2017, 07:06: PM

Expert Answer:

begin mathsize 16px style Given space that space straight A space and space straight B space are space two space independent space events.
We space know space that comma space straight A space and space straight B space are space two space independent space events comma space if space straight P left parenthesis straight A intersection straight B right parenthesis equals straight P left parenthesis straight A right parenthesis. straight P left parenthesis straight B right parenthesis
The space probability space of space occurrence space of space at space least space one space of space straight A space and space straight B
equals The space probability space of space occurrence space of space only space straight A space plus thin space The space probability space of space occurrence space of space only space straight B
plus The space probability space of space occurrence space of space straight A space and space straight B
equals Probability space of space occurrence space of space straight A space or space straight B
rightwards double arrow straight P left parenthesis at space least space one space of space straight A space and space straight B right parenthesis
equals straight P left parenthesis straight A union straight B right parenthesis
equals straight P left parenthesis straight A right parenthesis plus straight P left parenthesis straight B right parenthesis minus straight P left parenthesis straight A intersection straight B right parenthesis space
equals straight P left parenthesis straight A right parenthesis plus straight P left parenthesis straight B right parenthesis minus straight P left parenthesis straight A right parenthesis. straight P left parenthesis straight B right parenthesis
equals straight P left parenthesis straight A right parenthesis plus straight P left parenthesis straight B right parenthesis left square bracket 1 minus straight P left parenthesis straight A right parenthesis right square bracket
equals straight P left parenthesis straight A right parenthesis plus straight P left parenthesis straight B right parenthesis. straight P apostrophe left parenthesis straight A right parenthesis
equals 1 minus straight P apostrophe left parenthesis straight A right parenthesis plus straight P left parenthesis straight B right parenthesis. straight P apostrophe left parenthesis straight A right parenthesis
equals 1 minus straight P apostrophe left parenthesis straight A right parenthesis left square bracket 1 minus straight P left parenthesis straight B right parenthesis right square bracket
equals 1 minus straight P apostrophe left parenthesis straight A right parenthesis. straight P apostrophe left parenthesis straight B right parenthesis
Hence space proved.

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Answered by Rebecca Fernandes | 15th Mar, 2017, 09:03: PM