(Solved): Suppose you have a joint distribution over two random variables P(X,Y) where both X and Y take valu ...

Suppose you have a joint distribution over two random variables $P(X,Y)$ where both $X$ and $Y$ take values in the discrete set $\{a,b\}$. You know that the marginal distributions of the two variables are: $\begin{array}{ll}P(X=a)=0.8& P(X=b)=0.2\\ P(Y=a)=0.3& P(Y=b)=0.7\end{array}$ Suppose you also know that $X$ and $Y$ are independent. What is the probability of the event $P(X?=Y)$ ?