If $\overline{E}$ and $\overline{F}$ are the complementary events of events E and F respectively and if 0 < P(F) < 1, then
(a) $P(E/F) +P(\overline{E}/F)=1$
(b) $P(E/F) +P(E/\overline{F})=1$
(c) $P(\overline{E}/F) +P(E/\overline{F})=1$
(d) $P(E/\overline{F}) +P(\overline{E}/\overline{F})=1$
Answer & explanation
Correct answer: option 1
Since E/F and $\overline{E}/F$ are complementary events.
$∴P(E/F) +P(\overline{E}/F)=1$
Similarly, $ E/\overline{F}$ and $\overline{E}/\overline{F}$ are also complementary events.
$∴P(E/\overline{F}) +P(\overline{E}/\overline{F})=1$