Question

If a seed is planted, it has a 95% chance of growing into a healthy plant.If 8 seeds are planted, what is the probability that exactly 2 don't grow? Round your answer to three decimal places.

Answer 1

Solution

To find the probability that exactly 2 don't grow?

This is a binomial probability question. The "success" here is that the seed doesn't grow, so

p = 1 - 0.95 = 0.05 q=0.95 n=8 (number of repetitions) r =2 (number of success)

where

P = success

q = failure

$nC_r\text{ }p^r\text{ }q^{n-r}$$\begin{gathered} 8C_2.(0.05)^2(0.95)^{8-2} \\ 28(0.05^2)(0.95^6) \\ 0.05145 \\ \approx0.052\text{ \lparen3d.p\rparen} \end{gathered}$

Therefore the probability that exactly 2 don't grow = 0.052 (3d.p)