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 ?

Question

Let E , &#160; 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 &#8745; F &#8745; G ) = 1 10 For any event H , if H c denotes its complement, then which of the following statements is (are) TRUE ?

Aicharya · Accepted Answer

(i) P E &#8745; F &#8745; G c = P E &#8745; F - P E &#8745; F &#8745; G &#8804; P E - 1 10 = 1 8 - 1 10 = 1 40 (ii) P E c &#8745; F &#8745; G = P ( F &#8745; G ) - P ( E &#8745; F &#8745; G ) &#8804; P ( F ) - 1 10 = 1 6 - 1 10 = 1 15 (iii) P E &#8746; F &#8746; G &#8804; P E + P F + P G = 1 8 + 1 6 + 1 4 = 3 + 4 + 6 24 = 13 24 (iv) P E c &#8745; F c &#8745; G c max = 1 - P ( E &#8745; F &#8745; G ) min &#8757; P ( E &#8745; F &#8745; G ) min = 1 4 Thus P E c &#8745; F c &#8745; G c &#8804; 3 4

Let E ,   F and G be three events having probabilities P ( E ) = 1 8 , P ( F ) = 1 6 and P ( G ) = 1 4 …

Solution

Let E , &#160; F and G be three events having probabilities P ( E ) = 1 8 , P ( F ) = 1 6 and P ( G ) = 1 4 …

Solution

Let E , F and G be three events having probabilities P ( E ) = 1 8 , P ( F ) = 1 6 and P ( G ) = 1 4 …