What is the probability of drawing a face card from a regular deck of playing cards?

Answer 1

There are 52 cards in a standard playing card deck.

In such decks, there are four of each card:

Ace, Deuce (2), Trey (3), etc, through Ten,

and then there are the face (or picture) cards:

Jack, Queen, and King

(most card games remove the Joker from the deck,

so it will not included in this discussion).

Since there are a total of 12 face cards

(i.e., three types of picture cards multiplied by four of each type, or 3 x 4),

and assuming one is playing with a full deck (pun intended!),

then there are 12 out of 52 such cards,

so the probability of selecting a face card is 12-in-52,

or, reducing the terms, 3-in-13, or, roughly, 1-in-4.3.

So, if you were to randomly shuffle the deck,

and randomly remove 5 cards

(i.e., the closest whole number of cards to 4.3 that can be selected),

you could expect at least one of them to be a face card.

That does not mean that you WILL get a face card;

it only means that it is LIKELY.

As with any other math problem,

the "proof" may be found at the link, below,

from the University of Massachusetts.