Question

When randomly choosing two cards from a standard deck of cards without replacement, what is the probability of choosing a face card and then an ace? (Remember: standard deck has 52 cards, with 4 aces and 12 face cards)

A 3/221
B 3/168
C 4/221
D 9/169

Answer 1

The correct answer For K12 Quiz is C 4/221

because
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 "C" is the correct answer