Final answer:
The question is about calculating the probability that exactly one out of eleven planted seeds does not grow, using the binomial probability formula. By plugging the given probabilities into the formula, we find the desired probability.
Step-by-step explanation:
The student is asking about a probability problem involving binomial distribution. Specifically, they want to know the probability that exactly one out of 11 seeds planted does not grow into a healthy plant, given that each seed has a 70% chance of success (growing). To solve this, we use the binomial probability formula:
P(X = k) = C(n, k) * (p^k) * ((1-p)^(n-k))
Where P(X = k) is the probability of k successes in n trials, C(n, k) is the number of combinations of n items taken k at a time, p is the probability of success on a single trial, and (1-p) is the probability of failure on a single trial.
For this problem:
- n (total number of seeds) = 11
- k (number of seeds that do not grow) = 1
- p (probability of a seed growing) = 0.70
- 1-p (probability of a seed not growing) = 0.30
So, the calculations would be:
P(X = 1) = C(11, 1) * (0.70^10) * (0.30^1)
Calculating the combination C(11, 1) which is simply 11, and then raising the probabilities to their respective powers, we get:
P(X = 1) = 11 * (0.70^10) * (0.30)
After performing the multiplication, this gives us the exact probability that exactly one seed out of eleven planted does not grow.