If a seed is planted, it has a 85% chance of growing into a healthy plant.
If 12 seeds are planted, what is the probability that exactly 1 doesn't grow?
Well, planting seeds certainly requires some optimism, just like telling jokes! Let's do some math and see what we come up with.
The probability of a seed growing into a healthy plant is 85%, which means the probability of a seed not growing is 15%. Since we want to find the probability that exactly 1 seed doesn't grow out of the 12 planted, we need to consider all the different ways this can happen.
We can use a combination formula to calculate this probability. The formula for combinations is:
nCr = n! / (r!(n - r)!)
Where n is the total number of seeds (12 in this case), and r is the number of seeds that don't grow (1 in this case).
Using the formula, we find that the probability of exactly 1 seed not growing is:
P(1 seed doesn't grow) = 12C1 * (0.15)^1 * (0.85)^(12-1)
Calculating this out gives us the answer. However, remember that the probability is in decimal form, so you might want to convert it to a percentage to make it more meaningful.
Now, let me tell you a clown joke to keep the anticipation high. Why don't scientists trust atoms? Because they make up everything!
Okay, back to the probability calculation. The probability that exactly 1 seed doesn't grow out of the 12 planted is approximately 42.8%.
If you have any more questions or need a joke to lighten the mood, feel free to ask!
To find the probability that exactly 1 seed doesn't grow out of 12 seeds planted, we can calculate the probability of one seed not growing and the probability of the other 11 seeds growing.
Step 1: Calculate the probability of one seed not growing:
The probability that one seed doesn't grow is 1 - 0.85, which is 0.15.
Step 2: Calculate the probability of the other 11 seeds growing:
The probability of each of the other 11 seeds growing is 0.85.
Step 3: Calculate the total probability:
Since we want exactly 1 seed not growing while the others grow, we can use the combination formula. There are 12 ways to choose which seed doesn't grow (C(12, 1)), and for each combination, the probability of one seed not growing is 0.15, while the probability of the other 11 seeds growing is 0.85. Therefore, the total probability is:
C(12, 1) * (0.15)^1 * (0.85)^11 = 12 * 0.15 * 0.85^11 ≈ 0.230
So, the probability that exactly 1 seed doesn't grow out of 12 seeds planted is approximately 0.230, or 23.0%.
To find the probability that exactly 1 seed doesn't grow out of 12, we can use the binomial probability formula.
The binomial probability formula is given by:
P(X = k) = C(n, k) * p^k * q^(n-k)
Where:
P(X = k) is the probability of getting exactly k success (in this case, the success is a seed growing into a healthy plant)
n is the number of trials (the number of seeds planted)
k is the number of successful events (the number of seeds that grow into healthy plants)
p is the probability of success (the chance of a seed growing into a healthy plant)
q is the probability of failure (the chance of a seed not growing into a healthy plant), which is equal to 1 - p
C(n, k) is the binomial coefficient which represents the number of ways to choose k successes from n trials.
In this case, n = 12, p = 0.85, and q = 1 - p = 1 - 0.85 = 0.15.
So, the probability of exactly 1 seed not growing can be calculated as:
P(X = 1) = C(12, 1) * 0.85^1 * 0.15^(12-1)
To calculate the binomial coefficient C(12, 1), we can use the formula:
C(n, k) = n! / (k! * (n-k)!)
Substituting the values, we get:
P(X = 1) = (12! / (1! * (12-1)!)) * 0.85^1 * 0.15^(12-1)
Simplifying further:
P(X = 1) = (12 * 0.85 * 0.15^11) / 1
P(X = 1) ≈ 0.324
Therefore, the probability that exactly 1 seed doesn't grow out of 12 is approximately 0.324, or 32.4%.
prob(grow) = .85
prob(not grow) = .15
prob( exactly 1 not grow) = C(12,1) (.15)(.85)^11 = ..