Calculate the probability of event A using the Law of Total Probability given the following probabilities...

We are given the probabilities of events $B_1, B_2, B_3$ and the conditional probabilities of event $A$ given $B_1, B_2, B_3$.
$P(B_1) = 0.2$
$P(B_2) = 0.3$
$P(B_3) = 0.5$
$P(A|B_1) = 0.1$
$P(A|B_2) = 0.4$
$P(A|B_3) = 0.8$

Since $B_1, B_2,$ and $B_3$ form a partition of the sample space, the probability of event $A$ can be found using the Law of Total Probability:

The expression derived matches option A.