Joint Probability: Let X denote 'heads' and Y denote 'tails'

[abc4616]

Let X denote the number of heads and Y the number of tails when a coin is tossed 3 times. Assume that, for each toss, a head and tail are equally likely. Find the joint probability distribution of X and Y.

Does anyone know how to appoach this problem?

 

[pka]

\(\displaystyle \begin{array}{c}
{X|Y} & 0 & 1 & 2 & 3 \\
\hline
0 & 0 & 0 & 0 & {\frac{1}{8}} \\
1 & 0 & 0 & {\frac{3}{8}} & 0 \\
2 & 0 & {\frac{3}{8}} & 0 & 0 \\
3 & {\frac{1}{8}} & 0 & 0 & 0 \\
\end{array}\)