In a chess tournament, n games are being played, independently. Each game ends in a win for one player with probability 0.4 and ends in a draw (tie) with probability 0.6. Find the PMFs of the number of games ending in a draw, and of the number of players whose games end in draws.
For the first part, obviously, $X$ follows $B(n,0.6)$. For the second part, my understanding is that the number of players who draw, $Y$, is just $Y=2X$, and hence the PMF is:
$\mathbb{P}(Y=y) = \mathbb{P} (X=y/2) = \displaystyle{n \choose y/2}0.6^\frac y20.4^{n-\frac{y}{2}}$, for all non-negative integer values $y=2m$, $m=0(1)n$, and $0$ elsewhere.
Is this correct? Thank you in advance for your help.