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Math Help - 50/50 Chance

  1. #1
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    50/50 Chance

    Hello there folks!

    I was in a pretty serious debate with my friend about probability:

    You have 2 cards: 1 red and 1 blue.
    You have 1 chance to pick blue, then you mix the cards.
    It's either: you always pick blue, you pick blue n-times, you never pick blue.
    Let's say that time is infinite.

    How can I proove that you MUST pick blue at least once in infinite time?
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  2. #2
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  3. #3
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    Quote Originally Posted by Galaxy View Post
    Hello there folks!

    I was in a pretty serious debate with my friend about probability:

    You have 2 cards: 1 red and 1 blue.
    You have 1 chance to pick blue, then you mix the cards.
    It's either: you always pick blue, you pick blue n-times, you never pick blue.
    Let's say that time is infinite.

    How can I proove that you MUST pick blue at least once in infinite time?
    Why can't you keep getting red ?
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  4. #4
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    I'm sorry, I don't understand it. I'm still in high school.

    @Archie Meade
    I have to proove that you MUST, at least once in infinite time, get a blue card. The probability is 50/50, a 0.5 factor. If you aggregate 0.5 with 1/2 of 0.5 and repeat this forever, you will get number 1 (at least in infinite time). Can this be considered as a proof?
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  5. #5
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    The Law of Large Numbers: if you do an event over and over again, the results will tend to the average. The average is 50/50. Therefore, for example, if we do the event 100 times, our results should be roughly 50/50. We could have 45 blues and 55 red, 55 blue and 45 red, 49 blue and 51 red, ......
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  6. #6
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    Quote Originally Posted by Galaxy View Post
    I'm sorry, I don't understand it. I'm still in high school.

    @Archie Meade
    I have to proove that you MUST, at least once in infinite time, get a blue card. The probability is 50/50, a 0.5 factor. If you aggregate 0.5 with 1/2 of 0.5 and repeat this forever, you will get number 1 (at least in infinite time). Can this be considered as a proof?
    0.5+0.5^2+0.5^3+0.5^4+.................+0.5^n=\dis  playstyle\frac{0.5\left(1-0.5^n\right)}{0.5}

    approaches 1 as n approaches infinity.

    It's not a proof as such, because mathematically speaking, you cannot treat infinity as a value.
    You can calculate limits though.

    This is all ahead of you at present.

    The only way you "must" get a blue is if you can rule out, via some condition, a never-ending string of reds.
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