# Find the probability of drawing an ace followed by a non-face card with no replacement.?

### 3 Answers

- kingofclubs_ukLv 41 decade agoBest Answer
So assuming you are using a standeard 52 card deck:

Probability of an Ace = 4/52

There are 51 cards left in the deck, 12 of which are court cards - I assume this is what you mean by face cards?

So 51 - 12 = 39

Probability of a non face card = 39/51

So overall probability = (4*39)/(52*51) =0.0588 or 5.9%

The reason I disagree with the above answers is that to go aon to draw the second card, you HAVE to have drawn an Ace. You cannot take into account the possibility of not drawing an Ace as your first card in the calculation for the second card. Draw a tree diagram of possibilites, and you will see what I mean!

- 1 decade ago
there are 52 cards in a deck and four aces, so the probability of drawing an ace is 4/52, or 1/13. there are #1-10 non face cards, with four each, so 40. and since u already drew 1 card from the deck, there's a 40/51 chance to draw with no replacement. so 1/13 times 40/51 equals 40/663 :D

- DanLv 51 decade ago
There are 52*51 ways to draw two cards from a deck

there are 4* (8*4) ways to draw one of 4 aces followed by 8*4 non-faces cards.

p=4*8*4/52*51 =.04826546