Help find probability of drawing certaom cards from deck

[stuck_fugu]

Two cards are drawn without replacement from a standard deck of 52 cards. What is the probability that the first card is a face card and the second card is a queen?

I keep getting 7/221

but the answer says it's 11/663.


anyone know?

 

[Guest]

Re: Help quickly: probability of drawing cards.

Two cards are drawn without replacement from a standard deck of 52 cards. What is the probability that the first card is a face card and the second card is a queen?

I keep getting 7/221

but the answer says it's 11/663.


anyone know?

\(\displaystyle P(1st\ face\ \wedge\ 2nd Q)=P(1st\ K\ \vee\ N)P(2nd\ Q|1st\ K\ \vee\ N) + P(1st\ Q)P(2nd\ Q|1st\ Q)\)

(where \(\displaystyle \wedge\) should be read as "and", and \(\displaystyle \vee\) should be read as "or".

Now as there are four of each value of card in a deck and 52 cards:

\(\displaystyle P(1st\ K\ \vee\ N)=\frac{8}{52}\)

\(\displaystyle P(1st\ Q)=\frac{4}{52}\)

\(\displaystyle P(2nd\ Q|1st\ K\ \vee\ N)=\frac{4}{51}\)

\(\displaystyle P(2nd\ Q|1st\ Q)=\frac{3}{51}\).

And I'm sure you can do the final sum for yourself.

RonL

 

[mcrae]

you have 12 options to draw a face card of 52 cards in the deck
assume you dont draw a queen, theres 4 queens left of 51 cards in the deck
you take away four because there are four cases where the face card is a queen

12 * 4 - 4
------------
51 * 52

11/663 = 0.016591251