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| + | =[[MA375]]: The Principle of Induction= | ||
| + | Lecture Notes | ||
| + | ---- | ||
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If '''E''' and '''F''' are events in '''S''' (sample space) the the conditional probability of '''E''' and '''F''' is '''P(E|F) = P(E intersect F)'''. | If '''E''' and '''F''' are events in '''S''' (sample space) the the conditional probability of '''E''' and '''F''' is '''P(E|F) = P(E intersect F)'''. | ||
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note : if P(E|F) = P(E) | note : if P(E|F) = P(E) | ||
then P(F|E) = P(F) | then P(F|E) = P(F) | ||
| + | ---- | ||
| + | [[Main_Page_MA375Fall2008walther|Back to MA375, Fall 2008, Prof. Walther]] | ||
Revision as of 08:11, 20 May 2013
MA375: The Principle of Induction
Lecture Notes
If E and F are events in S (sample space) the the conditional probability of E and F is P(E|F) = P(E intersect F).
Further :
the conditional probability of "E" given "F" is =$ \frac {P(EnF)}{P(F)} $
defn: if P(E|F) = P(E) , then E and F are independent events otherwise they are dependant events.
note: independence implies that $ P(E)= P(E|F) = \frac {P(EnF)}{P(F)} $
or P(E).P(F)=P(EnF).
note : if P(E|F) = P(E)
then P(F|E) = P(F)
