Textbook Problem

Prove Bayes’ theorem for n=2. That is, prove that if a sample space S is a union of mutually disjoint events $B_1$ and $B_2$ if A is an event in S with $P\left(A\right)\ne 0$ , and $k=1$ or $k=2$ , then

$P\left(B_k|A\right)=\frac{P\left(A|B_k\right)P\left(B_k\right)}{P\left(A|B_1\right)P\left(B_1\right)+P\left(A|B_2\right)P\left(B_2\right)}.$