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  4. If E and F are events such that 0 < P(F) < 1, then

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Q. If $E$ and $F$ are events such that $0 < P(F) < 1$, then

Probability - Part 2

Solution:

$P\left(E\,|\,F\right) + P\left(\bar{E}\,| \,F\right)$
$= \frac{P\left(E\, \cap \,F\right)+P\left(\bar{E}\, \cap\, F\right)}{P\left(F\right)}$
$= \frac{P\left(\left(E \,\cup\, \bar{E}\right)\,\cap \,F\right)}{P\left(F\right)}$
$= \frac{P\left(F\right)}{P\left(F\right)} = 1$