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
`\frac{\binom{12}1}{\binom{52}1}=(12)/(52)`. Then the probability of drawing an ace second is
`\frac{\binom41}{\binom{51}1}=\frac4{51}`.

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


`(12)/(52)\cdot\frac4{51}=\frac4{221}`