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Math Help - probability of growing a healthy plant

  1. #1
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    probability of growing a healthy plant

    If a seed is planted, it has a 65% chance of growing into a healthy plant.

    If 10 seeds are planted, what is the probability that exactly 2 don't grow?

    I subtracted 1 from the probability that exaxtly 2 will grow , and my anwser is 1-.0042813781= 0.99572 ; is this correct , or do I have to do something else . Thanks in advance!!
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by skorpiox View Post
    If a seed is planted, it has a 65% chance of growing into a healthy plant.

    If 10 seeds are planted, what is the probability that exactly 2 don't grow?

    I subtracted 1 from the probability that exaxtly 2 will grow , and my anwser is 0.99572; is this correct , or do I have to do something else . Thanks in advance!!
    Note that if X represents the number of plants that grow, then it follows that X has a \mathcal{B}\left(10,.65\right) distribution.

    If we want to know the probability of exactly two plants failing to grow, its the same as asking for the probability of exactly eight plants that succeeded to grow.

    So it follows that the answer is P\left(X=8\right)={10\choose 8}\left(.65\right)^{10}\left(.35\right)^{10-8}\approx0.0742

    Does this make sense?
    Last edited by Chris L T521; August 2nd 2009 at 07:03 PM. Reason: fixed mistake
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  3. #3
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    This is a binomial distribution problem with n=10, p=.65

    We want to know the probability that 8 plants grow, so k=8

     <br />
P(k)={{n}\choose{k}}p^k(1-p)^{n-k}<br />

    <br />
P(8)={{10}\choose{8}}(.65)^8(1-.65)^{10-8}<br />

    {{n}\choose{k}} is notation for nCr in case you didnt know and you should be good from here
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  4. #4
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    thank you guys ; I got it. I guess I was thinking about normal distribution
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