Question

If a seed is planted, it has a 75% chance of growing into a healthy plant. If 8 seeds are planted, what is the probability that exactly 1 doesn't grow?

Answer 1

Step-by-step explanation

From the question, we can see that

Probability of sucess = 0.75

Probability of failure = 1-0.75=0.25

n=8

Therefore, we will use the binomial probability distribution formula to find the probability that exactly 1 doesn't grow

`P_x=(nCx)p^xq^(n-x)`

For exactly one not growing we must have seven success and one failure.

`\begin{gathered} P_7=8C7(0.75)^7(0.25)^1 \\ =(8!)/(7!1!)(0.75)^70.25 \\ =8(0.75)^7(0.25) \\ =0.2670 \end{gathered}`

Answer: 0.2670