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Math Help - Probability

  1. #1
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    Probability

    If seven flowerbeds are each planted with 20 seedlings find the probability that at least 12 seedlings mature in exactly five of the flowerbeds.

    Providing each seedling has a 0.7 chance of developing into a mature plant.
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  2. #2
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    Hello, BabyMilo!

    A seedling has a 0.7 probability of developing into a mature plant.
    Seven flowerbeds are each planted with 20 seedlings.

    Find the probability that at least 12 seedlings mature in exactly five of the flowerbeds.
    In any one particular flowerbed:

    . . \begin{array}{ccccc}<br />
P(\text{12 mature}) &=& {20\choose12}(0.7)^{12}(0.3)^8 \\ \\[-3mm]<br />
P(\text{13 mature}) &=& {20\choose13}(0.7)^{13}(0.3)^7 \\ \\[-3mm]<br />
P(\text{14 mature}) &=& {20\choose14}(0.7)^{14}(0.3)^6 \\<br />
\vdots && \vdots \\<br />
P(\text{19 mature}) &=& {20\choose19}(0.7)^{19}(0.3)^1 \\ \\[-3mm]<br />
P(\text{20 mature}) &=& {20\choose20}(0.7)^{20}(0.3)^0\end{array}


    The probability that at least 12 mature is the sum of the above probabilities.
    . . Call this sum S.

    We have a choice of 5 of the 7 flowerbeds: . {7\choose5}

    . . Therefore: . {7\choose5}\times S

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