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p(X<6)

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tullahbell | eNotes Newbie

Posted May 15, 2013 at 10:33 PM via web

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p(X<6)

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rakesh05 | High School Teacher | (Level 1) Assistant Educator

Posted May 18, 2013 at 7:08 AM (Answer #1)

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We know that probability of an event ranges between 0 and 1.

Now by the rule 

                     p(X<a)=1-p(X`>=a` ). Where X is a random variable

So              p(X<6)=1-p(X`>=` 6).

e.g. In throwing of dice experiment

         P(X<6)=P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)

                    =1/6+1/6+1/6+1/6+1/6

                   =5/6.

Here  we see 

           P(X`>=` 6)=P(X=6)=1/6.

So,       1-P(X`>=` 6)=1-1/6=5/6.

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