jmc

There are 52 possible outcomes, since there are 52 cards we can choose. There are 4 ways to choose a Queen, and there are 13 ways to choose a $♢$, but the outcomes are not mutually exclusive! We might choose the Queen of $♢$, which belongs to both outcomes. So we must subtract one to correct for this overcounting. Thus are are $17-1=16$ successful outcomes, and the probability is $\frac{16}{52}=\boxed{\frac{4}{13}}$.