SOLUTION: Let E and F be two events in S with P(E) = 0.42, P(F) = 0.52, and P(E &#8746; F) = 0.7. Find P(E &#8745; F) and P(E &#8745; FC). P(E &#8745; F) = P(E &#8745; F<sup>C</su

Algebra ->  Probability-and-statistics -> SOLUTION: Let E and F be two events in S with P(E) = 0.42, P(F) = 0.52, and P(E &#8746; F) = 0.7. Find P(E &#8745; F) and P(E &#8745; FC). P(E &#8745; F) = P(E &#8745; F<sup>C</su      Log On


   

Question 1125581: Let E and F be two events in S with P(E) = 0.42, P(F) = 0.52, and P(E ∪ F) = 0.7. Find P(E ∩ F) and P(E ∩ FC).
P(E ∩ F) =
P(E ∩ FC) =
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Let E and F be two events in S with
P(E) = 0.42,
P(F) = 0.52,
P(E ∪ F) = 0.7.
Find P(E ∩ F) and P(E ∩ FC). 
               P(E∪F) = P(E) + P(F) - P(E∩F)
                  0.7 = 0.42 + 0.52 - P(E∩F)
                  0.7 = 0.94 - P(E∩F)
         P(E∩F) + 0.7 = 0.94
               P(E∩F) = 0.24
---------------------------------------
                 P(E) = P(E∩F) + P(E∩FC)
                 0.42 = 0.24 + P(E∩FC)
                 0.18 = P(E∩FC)

Edwin