Help with probability

[drtdrums]

Helping a buddy with his prob and stats homework. He has a problem that's driving me nuts because I think I've done something wrong.

The problem:

You are playing a collectible card game (ed: like MTG or Pokemon or some other **** game). You have a deck of 120 cards. You draw 14 cards at the beginning of the game. To have a good chance at winning, you need to draw one of a particular type of card, Card X. You have 16 Card X's in your deck. What are the chances that you draw at least one Card X in the initial 14-card draw?

..

I'll hold my answer for now so that I don't influence the thought of anyone.

Thanks guys!

[DjTj]

There are 104 cards in your deck that are not card X.

The odds of drawing all 14 of your cards from that 104 is: 104/120 * 103/119 * 102/118 * ... * 91/107 = 11.9%

Thus the odds of drawing at least one Card X is 100% - 11.9% = 88.1%

[Corcaigh]

It's 1 - the probability of drawing no cards with an X

[drtdrums]

There are 104 cards in your deck that are not card X.

The odds of drawing all 14 of your cards from that 104 is: 104/120 * 103/119 * 102/118 * ... * 91/107 = 11.9%

Thus the odds of drawing at least one Card X is 100% - 11.9% = 88.1%

Beautiful. Thank you.

I was off...

Added the probabilities of drawing a card with an X together. Kinda crazy how it doesn't work...lol.

[PokerPacker]

I believe this is hypergeometric in nature, and you want to find the compliment.
the compliment:

(16) (104)
(0) *(14)
(120)
(14)

=
1*(104!/(104-14)!)
(120!/(120-14)!)

= 0.118783757

compliment of compliment = 0.881217243

[Corcaigh]

You can do it either way, but it amounts to the same.