So looking at a probability section in a textbook, it says that the sample space of drawing five cards from a deck of 52 is 52c5. But this confuses me because I would think that order matters. For example, when finding the sample space of two coin tosses it's HH, HT, TH, TT where the middle two are different even though the consist of the same elements. So I would think we would technically consider a one, two, three, four, five of hearts to be different from a two, one, three, four, five. So if I were to calculate the probability of a five-card hand being all hearts, I would think it would be 13/52 * 12/51 * 11/50 * 10/49 * 9/48 rather than (13c5)/(52c5)... Although now that I punch them each into a calculator, they agree on their value. I just don't see the logic here.
Also it says that, in a bag containing 4 green, 8 blue, and 5 red marbles, what are the ODDS that a marble selected is red? 5/12. My thinking is that it should be 5:12 which is equal to 5/17. Am I right about this?
In the case of the cards, the two cards are not drawn independently.
Originally Posted by ragnar
The first drawn effects the probability of the second card. That is true. But hands of cards are determined only by content not order of the deal.
In the case of a coin, the flips are independent.
What appears on the first does not effect the second.
So to model two flips we need four outcomes.