Question

A standard deck of cards consists of 52 cards.

Answer 1

This is interesting... it's a good thing I remember the actual question... you'll want to put that question back, @lxoe

Answer 2

Have to go now...
the question was what are the chances of the tenth card drawn being the ace of spades...
good luck everyone :D

Answer 3

From 51 cards (ie all the cards that aren't the ace of spades) choose 9 (leaving the tenth to be the ace of spades), divide by the total number of ways to choose 9 cards from 52.

That gives the probability of picking 9 cards w/o picking the ace of spades

Multiply that by 1/43 (if you know there's an A of spades in the remaining 43 cards, you have a 1/43 chance of getting it).

\[\large \frac{ 51C9 }{ 52C9 } \times \frac{ 1 }{ 43}\]

Answer 4

So, 1/52. Which makes sense, since this isn't a conditional probability problem. The chance of getting the A-spades on the 52nd draw is still 1/52, since you don't *know* that it wasn't chosen in the previous 51.

Change the question to "what are the chances of the tenth card drawn being the ace of spades, given that it was not chosen already" and the probability is then 1/43.

Just like the chance of getting the A-spades on the 52nd draw, given it was not chosen in the previous 51 draws, would be 100%, since it's the only card left!