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Math Help - Head & Tail problem

  1. #1
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    Head & Tail problem

    Say, I have unfair coin. When I toss it, probability of a head is 0.1, and probability of a tail is 0.9.

    I toss this coin 10 times. What is the probability I get 7 heads and 3 tails?

    I tried to draw a tree, but after 10 levels I gonna have 1024 branchs. My calculator has Pr and Cr functions, but I don't even know it's a Pr or Cr problem.

    Sorry I'm not a good math people.
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  2. #2
    Junior Member hoeltgman's Avatar
    Joined
    Aug 2005
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    You can solve this very easily if you know what the Bernoulli law is.
    You have two opposite results:
    Let's call the probability to get head: p = 0.1
    Let's call the probability to get tail: q = 0.9
    Since 1-0.9=0.1 the results are opposite. (First condition to apply Bernoulli Law)

    The number of times we toss the coin is called: n = 10
    Each toss is independant from the previous one. (Second condition to apply Bernoulli Law)
    Finally we call the number of times we get head: x
    In that case:
     P(x=7) = C^{7}_{10} \cdot 0.1^7 \cdot 0.9^3 = 8.748 \cdot 10^{-6}
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  3. #3
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    cheers,
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