Sample Space

1. Sep 16, 2007

EugP

1. The problem statement, all variables and given/known data
I'm having some trouble understanding how to write a sample space in a problem.
Here's an example:
Shuffle a deck of cards and turn over the first card. What is the sample space of this experiment? How many outcomes are in the event that the first card is a heart?

2. Relevant equations
$$C_k^n = {n \choose k} = \frac{n!}{k!(n - k)!}$$

3. The attempt at a solution
From what I was explained, sample space is the mutually exclusive and collectively exhaustive set of all possible outcomes. So in my case, wouldn't it be {2-A of hearts, 2-A of spades, 2-A of clubs, 2-A of diamonds} ? Those together create all the possiblities in the deck.
For the second part, isn't it simply 52 choose 13? If it is, it will just be

$${52 \choose 13} = \frac{52!}{13!(52 - 13)!} = 635,013,559,600 \approx 11 6.350135596 \cdot 10^{11}$$

But I'm not sure this is right. There are no answers in my book. If someone could help me on this it would be greatly appreciated.

2. Sep 16, 2007

matness

yes. You are right.
Sample space consists of all cards in the deck
and the answer of the second part is in mattmns 's post

Last edited: Sep 16, 2007
3. Sep 16, 2007

EugP

Thanks for verifying!

4. Sep 16, 2007

mattmns

I disagree with your second answer, I think it should be 13. The possible outcomes of a heart being the first card flipper over are A hearts, K hearts, ... , 2 hearts.