If a seed is planted, it has a 80% chance of growing into a healthy plant.
If 11 seeds are planted, what is the probability that exactly 1 doesn't grow?
To calculate the probability that exactly 1 seed doesn't grow out of 11 seeds planted, we can use the binomial probability formula.
The binomial probability formula is:
P(X = k) = (nCk) * p^k * (1 - p)^(n - k)
Where:
P(X = k) is the probability that exactly k seeds don't grow,
n is the total number of seeds planted (11 in this case),
k is the number of seeds that don't grow (1 in this case),
p is the probability of a single seed not growing (1 - 0.8 = 0.2 in this case),
nCk represents the number of ways to choose k seeds out of n.
Using the given values, we can substitute them into the formula:
P(X = 1) = (11C1) * (0.2)^1 * (1 - 0.2)^(11 - 1)
To calculate (11C1), we need to use the combination formula:
(11C1) = 11! / (1! * (11 - 1)!)
(11C1) = 11! / (1! * 10!)
Calculating the combinations:
(11C1) = 11
Now, substitute these values back into the formula:
P(X = 1) = 11 * (0.2)^1 * (0.8)^10
Calculating the probability:
P(X = 1) = 11 * 0.2 * 0.1073741824
P(X = 1) = 0.2359296
Therefore, the probability that exactly 1 seed doesn't grow out of 11 seeds planted is approximately 0.2359, or 23.59%.
To find the probability that exactly 1 seed doesn't grow out of 11 seeds planted, we need to use the concept of binomial probability.
The binomial probability formula is: P(X=k) = (nCk) * (p^k) * (q^(n-k))
Where:
P(X=k) is the probability of getting exactly k successes,
n is the number of trials,
k is the number of successes,
p is the probability of success in a single trial, and
q is the probability of failure in a single trial.
In this case:
n = 11 (11 seeds planted),
k = 1 (1 seed doesn't grow),
p = 0.8 (probability of a seed growing),
q = 1 - p = 1 - 0.8 = 0.2 (probability of a seed not growing).
Now, let's substitute these values into the formula:
P(X=1) = (11C1) * (0.8^1) * (0.2^(11-1))
To evaluate (11C1) or 11 choose 1, we use the combination formula:
(11C1) = 11! / (1! * (11-1)!)
= 11! / (1! * 10!)
= 11
Substituting this value into the formula:
P(X=1) = (11) * (0.8^1) * (0.2^(11-1))
= 11 * (0.8) * (0.2^10)
= 11 * 0.8 * 0.0001024
= 0.088064
Therefore, the probability that exactly 1 seed doesn't grow out of 11 seeds planted is approximately 0.0881, or 8.81%.
correction ... 11 * .2 * .8^10
it's the 2nd term of the binomial expansion