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

P(not E or not F or not G ) =

1 - P(E or F or G) = 1 - [P(E) + P(F) + P(G) - P(E and F) - P(E and G) - P(F and G) - P(E and F and G)] =

1 - [0.61 + 0.47 + 0.39 - 0.3 - 0.2 - 0.18 - 0.08] = 1 - 0.71 = 0.29.