Chapter 8.4, Problem 42E

In Problems $41$ and $42$, two halls are drawn in succession front an urn containing $m$ blue balls and $n$ white balls ( $m\ge 2\text{ and }n\ge 2$ ). Discuss the validity of each statement. If the statement is always true, explain why. If not, give $a$ counter example.

(A) If the two balls are drawn with replacement, then $P\left(B_1\left|W_2\right.\right)=P\left(W_2\left|B_1\right.\right)$.

(B) If the two balls are drawn without replacement, then $P\left(B_1\left|W_2\right.\right)=P\left(W_2\left|B_1\right.\right)$.