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Math Help - Probability Problem >> Very easy

  1. #1
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    Probability Problem >> Very easy

    I keep getting an error every time I try to do calculations with large numbers. I was wondering if there was another way to do these problems or a way to simplify them. As you can see, with smaller numbers I can put them into my calculator and get an answer:

    If you flip a coin 50 times, what is the chance you will get 25 heads?

    \frac{n!}{h!(h-n)!}(2^n)

    \frac{50!}{25!(50-25)!}(2^{-50}) = 0.11275

    But if I do a problem like this, I get the "OVERFLOW" error on my calculator and I can't do it:

    If you flip a coin 100 times, what is the chance you will get 50 heads?
    \frac{n!}{h!(h-n)!}(2^n)

    \frac{100!}{50!(100-50)!}(2^{-100}) = ?

    Is there another way to calculate the answer for the second problem so I don't get "OVERFLOW" in my calculator every time I try to do it?
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by Cursed View Post
    I keep getting an error every time I try to do calculations with large numbers. I was wondering if there was another way to do these problems or a way to simplify them. As you can see, with smaller numbers I can put them into my calculator and get an answer:

    If you flip a coin 50 times, what is the chance you will get 25 heads?

    \frac{n!}{h!(h-n)!}(2^n)

    \frac{50!}{25!(50-25)!}(2^{-50}) = 0.11275

    But if I do a problem like this, I get the "OVERFLOW" error on my calculator and I can't do it:

    If you flip a coin 100 times, what is the chance you will get 50 heads?
    \frac{n!}{h!(h-n)!}(2^n)

    \frac{100!}{50!(100-50)!}(2^{-100}) = ?

    Is there another way to calculate the answer for the second problem so I don't get "OVERFLOW" in my calculator every time I try to do it?
    Which calculator are you using?


    Try looking for a button which says \boxed{\text{nCr}}

    My humble Casio fx-82ES is capable of calculating it that way. (But not the other more elaborate way that you are using.)

    So if you use my way you will type:

    \boxed{\text{100}} \ \boxed{\text{nCr}} \ \boxed{\text{50}}

    Note: You might have to press \boxed{\text{Shift}} or \boxed{\text{2nd}} to access \boxed{\text{nCr}}
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