Suppose That $B _ { 1 }$ And $B _ { 2 }$

Multiple Choice

Suppose that $B _ { 1 }$ and $B _ { 2 }$ are mutually exclusive and complementary events, such that $P \left( B _ { 1 } \right) = .6$ and $P \left( B _ { 2 } \right) = .4$ . Consider another event $A$ such that $P \left( A \mid B _ { 1 } \right) = .2$ and $P \left( A \mid B _ { 2 } \right) = .5$ . Find $P \left( B _ { 1 } \mid A \right)$ .

A) $.625$
B) $.375$
C) $.240$
D) $.800$