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Math Help - archer probability

  1. #1
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    archer probability



    An archer hits the bullís eye 80% of the time. If he shoots 5 arrows, find the probability that he will get 4 bullís eyes

    to answer this question would you just multiply

    his success rate? ie

    .8 * .8 * .8 * .8 = 0.4096 so about 40 % chance with five
    arrows ?
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  2. #2
    Newbie opsahl92's Avatar
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    You have to multiply the probability of 4 hits and 1 miss (0.8^4(1-0.8)) with the number of ways this can happen in:

    Miss - Hit - Hit - Hit - Hit
    Hit - Miss - Hit - Hit - Hit
    Hit - Hit - Miss - Hit - Hit
    Hit - Hit - Hit - Miss - Hit
    Hit - Hit - Hit - Hit - Miss

    p(4 hits)=0.8^4(1-0.8)*5=40,96%

    So your answer is right (because 0.2*5=1), but try with another hit rate.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by opsahl92 View Post
    You have to multiply the probability of 4 hits and 1 miss (0.8^4(1-0.8)) with the number of ways this can happen in:

    Miss - Hit - Hit - Hit - Hit
    Hit - Miss - Hit - Hit - Hit
    Hit - Hit - Miss - Hit - Hit
    Hit - Hit - Hit - Miss - Hit
    Hit - Hit - Hit - Hit - Miss

    p(4 hits)=0.8^4(1-0.8)*5=40,96%

    So your answer is right (because 0.2*5=1), but try with another hit rate.
    The calculation you give does not have that answer, but the answer is correct. Each of the 5 ways of getter 4 hits has the same probability and so:

    p(4\text{ hits})= 5 \times 0.8^4 \times 0.2=0.4096

    or 40.96\%

    Equally you could observe that the probability of the number of hits has a binomial distribution B(5,0.8), and so:

    p(n\text{ hits})=b(n;5.0.8)

    which will give the same result when n=4.

    CB
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  4. #4
    Newbie opsahl92's Avatar
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    To avoid confusion for the thread starter, I just have to point out that there is nothing wrong with my calculation. I'll make it LaTeX though, for easy reading:

    p(\text{4 hits})=0.8^4\times(1-0.8)\times5=0,4096
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