Help find probability of drawing certaom cards from deck

stuck_fugu

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Jun 23, 2006
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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?
 
Re: Help quickly: probability of drawing cards.

stuck_fugu said:
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?


P(1st face  2ndQ)=P(1st K  N)P(2nd Q1st K  N)+P(1st Q)P(2nd Q1st Q)\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:

P(1st K  N)=852\displaystyle P(1st\ K\ \vee\ N)=\frac{8}{52}

P(1st Q)=452\displaystyle P(1st\ Q)=\frac{4}{52}

P(2nd Q1st K  N)=451\displaystyle P(2nd\ Q|1st\ K\ \vee\ N)=\frac{4}{51}

P(2nd Q1st Q)=351\displaystyle P(2nd\ Q|1st\ Q)=\frac{3}{51}.

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

RonL
 
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
 
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