<p>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?
A. 11/663</p>
<p>B. 3/169</p>
<p>C. 3/221</p>
<p>D. 4/221</p>
<p>I got A, but it took me a while to figure it out.</p>
<p>(12/52) = probability of drawing a facecard
since it is without replacement, if a queen is drawn the first time, the probability of drawing a queen the second time is (3/51); the probability of drawing a queen on the second card if a non-queen facecard was drawn the first time is (4/51). So...</p>
<p>(12/52)(8/12)(4/51) + (12/52)(4/12)(3/51)
^since there are 4 queens in a deck, there is a 8/12 probability that you will not draw the queen, which makes the probability of the second card being a queen (4/51); the (4/12) in the second part of this expression takes into account the probability of drawing a queen as the first card (4/12). Hope that helps, and I hope it is the correct answer.</p>