Rules of Probability

Question

Let E, F and G be three events in S with P(E) = 0.61, P(F) = 0.47, P(G) = 0.39, P(E ∩ F) = 0.3, P(E ∩ G) = 0.2, P(F ∩ G) = 0.18, and P(E ∩ F ∩ G) = 0.08. Find P(E^C ∪ F^C ∪ G^C).

P(E^C ∪ F^C ∪ G^C) 



Can't seem to figure it out. Any help is appreciated.

Answer 1

In order to solve this problem you need to use the property that P(A U B) = P(A) + P(B) - P(A ∩ B) and keep in mind that this can be expanded to 3 variables as well: P(A U B U C) = P(A U B) + P(C) - P(A ∩ B ∩ C). The other thing to keep in mind is that P(A^c U B^c) = 1 - P(A ∩ B). With these properties you can rewrite the probability using only information given in the problem.