If a seed is planted, it has a 85% chance of growing into a healthy plant. If 10 seeds are planted, what is the probability that exactly 2 don't grow?

Answer 1

Hi Emily,

This is another binomial case with "success" and "failure" albeit with an unorthodox definition. Here, success is defined as not growing. Recall the binomial equation:

P(X=x) = C(n,x)*p^x*q^n-x

n=total number of plants

x=desired number of plants that do not grow

p=probability of "success" (not growing)

q=probability of "failure" (growing)

The point is that we can define success and failure any way we want in the context of the problem. Here:

n= 10

x= 2

p= 0.15

q= 0.85

Notice that we used 0.15 as p, not 0.85. This is a potential trap. Remember we are interested in plants that do not grow.

P(X=2) = C(10,2)*0.15²*0.85⁸

C(10,2)= 10!/(2!*8!)

Do those calculations and you will have P(X=2), the probability that exactly two plants do not grow.