If a seed is planted, it has a 75% chance of growing into a healthy plant.
If 11 seeds are planted, what is the probability that exactly 2 don't grow?
To find the probability that exactly 2 out of 11 seeds don't grow, we need to use the binomial probability formula.
The binomial probability formula is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
P(X = k) is the probability of exactly 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.
n is the total number of trials.
In this case, we have:
k = 2 (exactly 2 don't grow)
n = 11 (11 seeds are planted)
p = 0.25 (probability that a seed doesn't grow)
Using the formula, the probability that exactly 2 out of 11 seeds don't grow can be calculated as follows:
P(X = 2) = C(11, 2) * (0.25)^2 * (1 - 0.25)^(11 - 2)
C(11, 2) = 11! / (2! * (11 - 2)!), which simplifies to 55.
Calculating the probability:
P(X = 2) = 55 * (0.25)^2 * (0.75)^9 ≈ 0.0133
Therefore, the probability that exactly 2 out of 11 seeds don't grow is approximately 0.0133, or 1.33%.
To calculate the probability of events occurring, you can use the concept of binomial probability. In this case, we want to find the probability that exactly 2 seeds out of 11 do not grow.
The probability of a single seed not growing is 1 - 0.75 = 0.25 (since it has a 75% chance of growing).
The formula to calculate the binomial probability is:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
Where:
- n is the total number of trials (in this case, the number of seeds planted, which is 11)
- k is the number of successful trials (in this case, the number of seeds not growing, which is 2)
- p is the probability of success in a single trial (in this case, the probability of a seed not growing, which is 0.25)
Using this formula, we can calculate the probability as follows:
P(X = 2) = (11 choose 2) * 0.25^2 * (1 - 0.25)^(11 - 2)
To calculate "(11 choose 2)", we use the combination formula:
(11 choose 2) = 11! / (2!(11 - 2)!) = (11 * 10) / (2 * 1) = 55
Now we can substitute the values into the probability formula:
P(X = 2) = 55 * 0.25^2 * (1 - 0.25)^(11 - 2)
Calculating this:
P(X = 2) = 55 * 0.25^2 * 0.75^9 ≈ 0.273
Therefore, the probability that exactly 2 seeds out of 11 do not grow is approximately 0.273 or 27.3%.
prob(success) = 3/4
prob(fail) = 1/4
prob(2 of 11 to fail)
= C(11,2)(1/4)^2 (3/4)^9
= .258
check my arithmetic