SOLUTION: Let E, F be events; p(E)= 0.6, p(F)= 0.4, p(E and F)= .15 Find p(E or F) Find p(E^c) Find p(E and F^c)

Algebra ->  Probability-and-statistics -> SOLUTION: Let E, F be events; p(E)= 0.6, p(F)= 0.4, p(E and F)= .15 Find p(E or F) Find p(E^c) Find p(E and F^c)       Log On


   

Question 1145319: Let E, F be events; p(E)= 0.6, p(F)= 0.4, p(E and F)= .15
Find p(E or F)
Find p(E^c)
Find p(E and F^c)
Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
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(a)  p(E or F) = apply the general formula     = p(E) + P(F) - p(E and F) = 


               = now substitute the given data = 0.6 + 0.4 - 0.15 = 0.85.    ANSWER




(B)  p(E^c) = the complement to p(E) = 1 - p(E) = 1 - 0.6 = 0.4.             ANSWER




(C)  the set ( E and F^c)  consists of those elements of E that do not belong to F.

     In other words,  ( E and F^c)  is  E \ (E and F).


     Therefore,  p(E and F^c) = p(E) - p(E and F) = 0.6 - 0.15 = 0.45.       ANSWER

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All questions answered -- the problem is solved.