Drawing 2 cards from a shuffled deck, what is the probability that the first is a spade and the second is an ace?
I was thinking that we'd do $\frac{13}{52} \cdot (\frac{4}{51} + \frac{3}{51})$, since the first card could have been an ace. Is this correct?
Best Answer
So the probability that the first card is a non-ace spade is $12/52$, and the probability that we pull an ace after that is $4/51$. On the other hand, the probability that we draw the ace of spades is $1/52$, and the chance of pulling another ace is $3/51$. All together we have
$$\frac{12}{52}\cdot\frac{4}{51}+\frac{1}{52}\cdot\frac{3}{51}$$