There are 3 kinds of face cards, jacks, queens, and kings, and four suits of
each which makes 3*4=12 face cards in a 52-card deck. So there are 52-12=40
non-face cards.
When you see the words "at least one", always first find the probability of the
so-called complement event, the event of failing. That is, we find the
probability of completely failing to get any face cards at all and then subtract
from 1 to get the probability of succeeding (getting at least one face card).
The number of ways he can fail, that is, to draw four cards from just the 40
non-face-cards, is C(40,4) = 91390 ways.
The number of ways he can draw any four cards from the entire 52-card deck is
C(52,4) = 270725 ways.
So the probability of failing to get a face card is to get one of the 91390 ways
to fail out of the 270725 ways to get any four cards.
That's a probability of failing of 91390/270725 which reduces to 1406/4165,
which is approximately the decimal 0.33757503.
So the probability of succeeding is that probability subtracted from 1 and
1 - 1406/4165 is 2759/4165 which is about 0.66242497 or 66.2%.
Edwin
