Events $A_1$, $A_2$ and $A_3$ form a partiton of the sample space S with probabilities $P(A_1) = 0.1$, $P(A_2) = 0.3$, $P(A_3)= 0.6$.
If E is an event in S with $P(E|A_1) = 0.1$, $P(E|A_2) = 0.5$, $P(E|A_3) = 0.8$, compute

$P(E) =$
$P(A_1|E) =$
$P(A_2|E) =$
$P(A_3|E) =$