# Probability Theory

1. Jan 21, 2007

I got it.

Stumped on this question:
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?

Attempt at a solution:

$$D = \{$$ deck of 52 cards randomly shuffled $$\}$$
$$S = \{ x | x \in D \}$$

I'm not sure if this is right. The event is viewing the the first card. So if we are viewing one card, all possible cards viewable at one time would just be one of the 52 cards right? Or does the sample space need for example:

S = {D-H2, D-H3, ... D-HA, D-***,}
Where D is the 52 cards. H2 would mean two of hearts, HA would mean ace of hearts. *** would mean all other card combinations.

Next part,
"How many outcomes are in the event that the first card is a heart"

Would I define the event as,
E_H = { D-H2, D-H3, ... , D-HK, D-HA }
D-H2 would mean the set that contains 51 cards without the two of hearts.

Thus the number of elements of E_H would be: 51^13

Last edited: Jan 21, 2007
2. Jan 21, 2007

### mattmns

You said you got it, but what you have there is not right? You should have only 13 outcomes (for the first card being a heart). The event space would just be {2h, 3h, ... 10h, Jh, Qh, Kh, Ah} where 2h = 2 of hearts, etc.

3. Jan 21, 2007