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Math Help - Describing a Probability Space

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    Describing a Probability Space

    So there's something I just haven't been able to figure out, or haven't had a good answer to, with regard to probability. I've accepted that, in a coin toss, we distinguish between the scenario Heads-Tails and Tails-Heads, even though both of these are basically just getting one Head and one Tail. However, when we then deal with decks of cards, we don't distinguish between being dealt A-Q-K-J-(10) of hearts and being dealt (10)-A-Q-K-J. Why? I get that in the deck of cards thing order doesn't matter, these are the same hand, but then why should it matter with coin tosses? We intuitively think that Heads-Tails is, by the same logic, identified with Tails-Heads.
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    MHF Contributor matheagle's Avatar
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    You can use either order or non-order when listing events.
    However, the simple events may not be equally likely.
    In tossing a pair of dice, it's better to use order.
    Otherwise you may think that obtaining (1,1) is as likely as (1,2)
    which it isn't.
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    Whoa, whoa, whoa, rolling a (1, 1) is not equally likely as rolling (1, 2)? I assume here that this means rolling a 1, then a 1. Two independent events on a fair six-sided die? Or is the die not fair? If not, I don't see how this illustrates the point.

    Also, I guess I should be satisfied with my main question, since I see how you can use order in the case of cards, it's just more complicated computations. But it makes me wonder:

    I can ignore order with cards if I want to. Why can I not do the same with flipping two coins? I'm just not seeing why it is that you can treat one in one way and not treat the other in the same way.
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    Quote Originally Posted by ragnar View Post
    Whoa, whoa, whoa, rolling a (1, 1) is not equally likely as rolling (1, 2)? I assume here that this means rolling a 1, then a 1. Two independent events on a fair six-sided die? Or is the die not fair? If not, I don't see how this illustrates the point.

    Also, I guess I should be satisfied with my main question, since I see how you can use order in the case of cards, it's just more complicated computations. But it makes me wonder:

    I can ignore order with cards if I want to. Why can I not do the same with flipping two coins? I'm just not seeing why it is that you can treat one in one way and not treat the other in the same way.
    One is sampling with replacement and the other is sampling without replacement.

    CB
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