Solution
= Solution
Because the $B_i$ partition the <sample space>, the events $A\cap B_i$ are disjoint and their union is $A$. Finite additivity and the definition of <conditional probability> give the <law of total probability>
$$
\boxed{\mathbb P(A)=\sum_{i=1}^{k}\mathbb P(A\mid B_i)\mathbb P(B_i)}.
$$
The assumption $\mathbb P(B_i)>0$ ensures that each conditional probability is defined.