Answer
$\frac{1}{9}$
Work Step by Step
Because the tiles are replaced, the events are independent:
4 of the 12 tiles are Y's:
P(Y)=$\frac{4}{12}$=$\frac{1}{3}$
4 of the 12 tiles are Y's:
P(Y after Y)=$\frac{4}{12}$=$\frac{1}{3}$
P(Y then Y)=P(Y) $\times$ P(Y after Y)
P(Y then Y)=$\frac{1}{3}$ $\times$ $\frac{1}{3}$= $\frac{1}{9}$
