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# Two cards are drawn without replacement from a standard deck of 52 cards. What is the probability that one of the cards is a face card (Jack, Queen, or King)

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Two cards are drawn without replacement from a standard deck of 52 cards. What is the probability that one of the cards is a face card (Jack, Queen, or King) and the other is a 9, and are these events independent?

A. 4/221; no, they are dependent events
B. 3/169; yes, they are independent events
C. 1/24; yes, they are independent events
D. 8/221; no, they are dependent events

Apr 19, 2016

#1
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I got 3/169 or B.

I don't know if they are independent or dependent

Apr 19, 2016
#2
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I come up with  "A"  4/221 and they are dependent

Apr 19, 2016
#3
+128794
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There are 12 face cards......so

The probability of drawing one on the first draw = 12/52

And the probability of drawing a "9" on the second draw  = 4/51

So the probability  = (12/52) * (4/51)  = 4/221

These are dependent events....let A be the probability of drawing a face card and let B be the probabilitiy of drawing "9'....then...

P (A ∩ B)  = 0      in other words......there is no face card that is also a "9"

So...independent events have the relationship that

P(A ∩ B)  must equal P(A) * P(B)...but

0 ≠  4/221

So...... "A"  is the correct answer

Apr 19, 2016