Let E ,   F and G be three events having probabilities P ( E ) = 1 8 , P ( F ) = 1 6 and P ( G ) = 1 4 , and let P ( E ∩ F ∩ G ) = 1 10 For any event H , if H c denotes its complement, then which of the following statements is (are) TRUE ?
C. P ( E ∪ F ∪ G ) ≤ 13 24
(i) P E ∩ F ∩ G c = P E ∩ F - P E ∩ F ∩ G ≤ P E - 1 10 = 1 8 - 1 10 = 1 40 (ii) P E c ∩ F ∩ G = P ( F ∩ G ) - P ( E ∩ F ∩ G ) ≤ P ( F ) - 1 10 = 1 6 - 1 10 = 1 15 (iii) P E ∪ F ∪ G ≤ P E + P F + P G = 1 8 + 1 6 + 1 4 = 3 + 4 + 6 24 = 13 24 (iv) P E c ∩ F c ∩ G c max = 1 - P ( E ∩ F ∩ G ) min ∵ P ( E ∩ F ∩ G ) min = 1 4 Thus P E c ∩ F c ∩ G c ≤ 3 4
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