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Please answer this question:

when I enter school,3 of 4 times i use the main door. when i leave school,i use the main door only 1 of3 times. on any given daywhat is the probablitythat i both enter and leave by the main door?



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The events  "Entering school through the main door" and "Leaving by main door" are independent.  Outcome of second event does not depend on outcome of 1st event.
Label them  event A and B.    P(A) = 3/4      P(B) = 1/3
So P(B / A )  =  P (A) * P(B)         as P(A intersection B) is 0.

Answer is 3/4  *  1/3  = 1/4

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