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

Guest Apr 19, 2016

#3**0 **

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

CPhill Apr 19, 2016