Question

If a seed is planted, it has a 80% chance of growing into a healthy plant. If 8 seeds are planted, what is the probability that exactly 3 don't grow?

Answer 1

Given that a seed that is planted has an 80% chance of growing into a healthy plant, and knowing that you have to find the probability that exactly 3 seeds of 8 seeds planted don't grow, you need to use this Binomial Distribution Formula:

$P(x)=\frac{n!}{(n-x)!x!}\cdot p^x(1-p)^{n-x}$

Where "n" is the number of trials, "x" is the number of successes desired, and "p" is the probability of getting a success in one trial.

In this case, you can identify that:

$p=100\text{\%}-80\text{\%}=20\text{\%}=0.20$$\begin{gathered} n=8 \\ x=3 \end{gathered}$

Now you can substitute values into the formula and evaluate:

$P(3)=(\frac{8!}{(8-3)!3!})(0.20)^3(1-0.20)^{8-3}$$P(3)=\frac{57344}{390625}\approx0.1468$

Hence, the answer is:

$P(3)\approx0.1468$