Answer
$\frac{2}{3}$
Work Step by Step
Probability that at least one of the two events occurs is $= P(A \cup B)$.
The event that at most one occurs is $(A \cap B)^c$.
The probability that at least one of the two events occurs given at most one occurs is
$P ((A \cup B)|((A \cap B)^c))$.
We have:
$P((A \cup B)|((A \cap B)^c)) = \frac{P((A \cup B) \cap ((A \cap B)^c))}{P((A \cap B)^c)}$
= $\frac{P(A \cap B^c) + P(A^c \cap B)}{P(A \cap B^c) + P(A^c \cap B) + P((A \cup B)^c)}$
= $\frac{0.1+0.3}{0.1+0.3+0.2} = \frac{0.4}{0.6} = \frac{2}{3}$
