jee-advanced 1998 Q29

jee-advanced · India Conditional Probability Proof of a General Conditional Expectation or Independence Property

29. If $\vec { E }$ and $\vec { F }$ are the complementary events of events $E$ and $F$ respectively and if $0 < \mathrm { P } ( \mathrm { F } ) < 1$, then.
(A) $\quad P ( E / F ) + P ( \vec { E } / F ) = 1$
(B) $\quad P ( E / F ) + P ( E / \vec { F } ) = 1$
(C) $\mathrm { P } ( \vec { E } / \mathrm { F } ) + \mathrm { P } ( \mathrm { E } / \vec { F } ) = 1$
(D) $\quad \mathrm { P } ( \mathrm { E } / \vec { F } ) + \mathrm { P } ( \vec { E } / \vec { F } ) = 1$

29. If $\vec { E }$ and $\vec { F }$ are the complementary events of events $E$ and $F$ respectively and if $0 < \mathrm { P } ( \mathrm { F } ) < 1$, then.\\
(A) $\quad P ( E / F ) + P ( \vec { E } / F ) = 1$\\
(B) $\quad P ( E / F ) + P ( E / \vec { F } ) = 1$\\
(C) $\mathrm { P } ( \vec { E } / \mathrm { F } ) + \mathrm { P } ( \mathrm { E } / \vec { F } ) = 1$\\
(D) $\quad \mathrm { P } ( \mathrm { E } / \vec { F } ) + \mathrm { P } ( \vec { E } / \vec { F } ) = 1$\\

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