If a seed is planted, it has a 84% chance of growing into a healthy plant.
If 12 seeds are planted, what is the probability that exactly 4 don't grow?

Step 1 ：We are given a problem where a seed has an 84% chance of growing into a healthy plant. We are asked to find the probability that exactly 4 out of 12 seeds don't grow into a healthy plant. This is a binomial probability problem.

Step 2 ：In a binomial probability problem, we have two possible outcomes. In this case, the outcomes are the seed grows into a healthy plant (success) or it doesn't (failure). The probability of success is given as 84% or 0.84. Therefore, the probability of failure is 1 - 0.84 = 0.16.

Step 3 ：The formula for binomial probability is: \(P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\), where \(P(X=k)\) is the probability we want to find, \(C(n, k)\) is the number of combinations of n items taken k at a time, p is the probability of success, n is the number of trials, and k is the number of successes we want to find the probability for.

Step 4 ：In this case, n=12, k=8, and p=0.84. We calculate the number of combinations, \(C(n, k)\), to be 495. We then calculate \(p^k\) to be approximately 0.2479 and \((1-p)^(n-k)\) to be approximately 0.000655.

Step 5 ：Substituting these values into the binomial probability formula, we find the probability to be approximately 0.0804.

Step 6 ：Final Answer: The probability that exactly 4 out of 12 seeds don't grow into a healthy plant is approximately \(\boxed{0.0804}\) or \(\boxed{8.04\%}\).