If `barE` and `barF` are the complementary events of E and F respectively and if `0 < P(F)<1`, then

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If `barE` and `barF` are the complementary events of E and F respectively and if `0 < P(F)<1`, then

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answered Nov 13, 2021 by JackTerrance

Best answer

Correct Answer - A::B (a)P(E/F)+P( ˉ E /F)= P(E∩F) P(F) + P( ˉ E ∩F) P(F) = P(E∩F)+P( ˉ E ∩F) P(F) = P(F) P(F) =1 Therefore, option (a) is correct. (b)P(E/F)+P(E/ ˉ F )= P(E∩F) P(F) + P(E∩ ˉ F ) P( ˉ F ) = P(E∩F) P(F) +(P E∩ ˉ F 1-P(F) ≠1 Therefore, option (b) is not correct. (c)P( ˉ E /F)+P(E/ ˉ F )= P( ˉ E ∩F) P(F) + P(E∩ ˉ F ) P( ˉ F ) = P( ˉ E ∩F) P(F) + P(E∩ ˉ F ) 1-P(F) ≠1 Therefore, option (c) is not correct. (d)P(E/ ˉ F )+P( ˉ E / ˉ F )= P(E∩ ˉ F ) P( ˉ F ) + P( ˉ E ∩ ˉ F ) P( ˉ F ) = (P(bar(F)))/(P(bar(F))) = 1 Therefore, option (d) is correct.

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