Question

When randomly choosing two cards from a standard deck of cards without replacement, what is the probability of choosing a face card and then an ace? (Remember: standard deck has 52 cards, with 4 aces and 12 face cards)
a)3/221
b)3/169
c)4/221
d)9/169

Answer 1

There are 12 face cards and 4 aces to choose from. For the first card, the probability of drawing a face is $\dfrac{\binom{12}1}{\binom{52}1}=\dfrac{12}{52}$. Then the probability of drawing an ace second is $\dfrac{\binom41}{\binom{51}1}=\dfrac4{51}$.

So the probability of drawing these two particular cards in the given order is

$\dfrac{12}{52}\cdot\dfrac4{51}=\dfrac4{221}$