JEE Advanced 2007 Paper 2Question 1
Let $E^c$ denote the complement of an event $E$. Let $E,F,G$ be pairwise independent events with $P(G)>0$ and $P(E\cap F\cap G)=0$. Then $P(E^c\cap F^c\,|\,G)$ equals
Probability
Solution
$P(E^c\cap F^c\cap G)=P(G)-P(E\cap G)-P(F\cap G)+P(E\cap F\cap G)=P(G)(1-P(E)-P(F))$. Dividing by $P(G)$ gives $1-P(E)-P(F)=P(E^c)-P(F)$.