What is the probability that the ace of spades is at the bottom of a standard deck of 52 cards given that the ace of hearts is not at the top?
I asked my older brother, and he said it should be $\frac{50}{51} \cdot \frac{1}{51}$ because that's $\mathbb{P}(A\heartsuit \text{ not at top}) \times \mathbb{P}(A\spadesuit \text{ at bottom}),$ but I'm not sure if I agree. Shouldn't the $\frac{50}{51}$ be $\frac{50}{52}$?
Thanks you!