note06 - Section 2.3 Conditional Probability and...

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Section 2.3: Conditional Probability and Independence The conditional probability of event A given B , where p ( B ) negationslash = 0, is the proba- bility that event A occurs given that event B has occurred. P ( A | B ) = P ( A B ) P ( B ) The multiplicative rule is simply the conditional probability rule rewritten. P ( A B ) = P ( A | B ) · P ( B ) or P ( A B ) = P ( B | A ) · P ( A ) Two events A and B are independent if P ( A | B ) = P ( A ) or P ( B | A ) = P ( B ) , as long as P ( A ) and P ( B ) does not equal to 0. A and B are said to be independent if the occurrence of one does not affect the probability of the occurrence of other. Exercise 1. Show that p ( A B ) = P ( A ) · P ( B ) if A and B are independent.
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2. The probability that a microchip fails on its first use is 0 . 10. Given that a microchip lasts through its first use, the probability that it lasts a year is 0 . 99. What is the probability that the chip does not fail during its first year (including first use)?
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