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Thread: Statisics

  1. #1
    Newbie CaptainAmerica97's Avatar
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    Statisics

    Can someone please help me with the this math problem:

    If a seed is planted, it has a 70% chance of growing into a healthy plant.
    If 8 seeds are planted, what is the probability that exactly 1 doesn't grow?
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  2. #2
    MHF Contributor
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    Re: Statisics

    The number of healthy plants has a binomial distribution with $n=8,~p=0.7$

    $P[\text{1 plant doesn't grow}] = P[\text{7 plants grow}] = \dbinom{8}{7}(0.7)^7(1-0.7)^1 = \dfrac{2470629}{12500000} = 0.19765$
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  3. #3
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    Re: Statisics

    Writing "G" for "grows" and "N" for "does not grow", this can happen as
    NGGGGGGG
    GNGGGGGG
    GGNGGGGG
    GGGNGGGG
    GGGGNGGG
    GGGGGNGG
    GGGGGGNG
    GGGGGGGN

    In other words, there are 8 possible orders. That is reflected in Romsek's \begin{pmatrix} 8 \\ 7\end{pmatrix}= \frac{8!}{7!1!}= 8. The probability of "NGGGGGGG" is, of course, (.3)(.7)^7= 0.02471, approximately, and it is easy to see that the probability of "GNGGGGGG", etc is exactly the same- you have the same numbers, just in a different order. So the probability of all 8 orders is 8(0.02471)= 0.19768.
    Last edited by HallsofIvy; Nov 15th 2017 at 04:18 PM.
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