SOLUTION: If a seed is planted, it has a 65% chance of growing into a healthy plant. If 11 seeds are planted, what is the probability that exactly 4 don't grow?

Algebra ->  Probability-and-statistics -> SOLUTION: If a seed is planted, it has a 65% chance of growing into a healthy plant. If 11 seeds are planted, what is the probability that exactly 4 don't grow?      Log On


   

Question 1145729: If a seed is planted, it has a 65% chance of growing into a healthy plant.
If 11 seeds are planted, what is the probability that exactly 4 don't grow?
Answer by ikleyn(52775) About Me  (Show Source):
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This is a binomial distribution type problem where p(x) = C(n,x)* p^x * q^(n-x)


    n is equal to 11                    // number of trials
    x is equal to  4                    // number of success trials
    p is the probability of don't grow
    q = 1 - p
    C(n,x) = n! / (x! * (n-x)!)         // binomial coefficient


Notice that the "success" in this case is getting "don't grow" with the probability p = 1 - 0.65 = 0.35.


Thus in your case  p(4, 11, 0.35) = C(11,4) * 0.35^4 * 0.65^7 = use Excel function BINOM.DIST(4, 11, 0.35, FALSE) = 0.243.    ANSWER


On Excel function BINOM.DIST, see its description everywhere, for example

https://support.office.com/en-us/article/binom-dist-function-c5ae37b6-f39c-4be2-94c2-509a1480770c