what is the probability of drawing 2 cards in succession

Question

What is the probability of drawing 2 cards in succession (without replacement) from a standard deck and having them both be face cards? Round to the nearest thousandth.

Answer 1

There are 4 suits, each having:

A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K (13 total cards per suit)

The face cards are J, Q, K (3 cards per suit)

So 13 cards x 4 suits = 52 total cards.

And, since there are 3 face cards in each suit, there are a total of 12 face cards (3 face cards per suit x 4 suits = 12 face cards).

So, for the first draw, the probability of getting a face card is 12/52 or 3/13.

For the second draw, since you have already drawn a face card, there are now 51 total cards left with 11 face cards making the probability of drawing a face card on the second draw 11/51.

1st draw: 3/13

2nd draw: 11/51

Total probability = (3/13)(11/51) = 33/663 or 11/221