If a seed is planted, it has a 70% chance of growing into a healthy plant.

If 7 seeds are planted, what is the probability that exactly 1 doesn't grow?

Here What I did I thought its premutation but some reason I got that wrong, I multiple by (0.10) and (0.70) of the seeds I still got it wrong. Where did I got it wrong

Well, it seems like the seeds are being a little picky about their growing conditions! Let's think about this problem in terms of probability.

To find the probability that exactly 1 seed doesn't grow, we need to consider the different scenarios in which this can happen.

We can imagine that the 7 seeds are being planted in a row. The seed that doesn't grow can be any one of the 7 seeds, so we have 7 possibilities.

For each scenario, the probability of a seed not growing is 30% (since it has a 70% chance of growing). So, the probability of exactly 1 seed not growing is:

P(1 seed doesn't grow) = (0.3) * (0.7)^6

Now we multiply this probability by the number of possibilities (7) to get the final result:

P(exactly 1 seed doesn't grow) = 7 * (0.3) * (0.7)^6

And if you crunch the numbers, you should get the probability you're looking for. Good luck with your seeds!

To calculate the probability that exactly 1 seed out of 7 doesn't grow, 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 k successes
- C(n, k) is the number of combinations of n items taken k at a time
- p is the probability of success
- q is the probability of failure (1 - p)
- n is the total number of trials

In this case, n = 7 (7 seeds planted), p = 0.7 (probability of a seed growing), and q = 1 - p = 1 - 0.7 = 0.3 (probability of a seed not growing).

Now, let's calculate the probability that exactly 1 seed doesn't grow.

P(X=1) = C(7, 1) × (0.7)^1 × (0.3)^(7-1)

Using the combination formula C(7, 1) = 7, we have:

P(X=1) = 7 × 0.7^1 × 0.3^6

P(X=1) = 7 × 0.7 × 0.3^6

P(X=1) = 0.00033075

Therefore, the probability that exactly 1 out of 7 seeds doesn't grow is approximately 0.00033075, or about 0.033075%.

To find the probability that exactly 1 seed out of 7 doesn't grow, we can use the binomial probability formula. The formula to find the probability of k successes in n trials is:

P(k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:
- P(k) is the probability of getting k successes
- n is the total number of trials (seeds planted)
- k is the number of successful trials (seeds that grow)
- p is the probability of success (the seed growing)
- (1 - p) is the probability of failure (the seed not growing)

In this case, there are 7 seeds planted, and each seed has a 70% chance of growing (0.70). The probability that a seed doesn't grow is the complement of the probability that it does grow, which is 1 - p, or 1 - 0.70 = 0.30.

So, to find the probability that exactly 1 seed doesn't grow out of the 7 seeds planted, we substitute these values into the formula:

P(1) = C(7, 1) * (0.70)^1 * (0.30)^(7 - 1)

Now, let's calculate it step-by-step:

C(7, 1) = 7! / (1! * (7 - 1)!) = 7

Therefore, P(1) = 7 * (0.70)^1 * (0.30)^(7 - 1)
= 7 * 0.70 * 0.30^6
≈ 7 * 0.70 * 0.000729

By calculating this, we find that P(1) is approximately 0.01536, or 1.536%.

Therefore, the probability that exactly 1 seed doesn't grow out of the 7 seeds planted is approximately 0.01536 or 1.536%.

No, this is an example of Binomial Distribution.

You are planting 7 plants, and you want the prob that exactly 1 does not grow.

Suppose it is the 3rd plant which did not grow.
GGNGGGG, where G stands for grow, N for not grow.
That specific probability is
(.7)(.7)(.3)(.7)(.7)(.7)(.7)
= (.7^6)(.3)

but it could have been 7 different arrangements of G's and N
e.g.
GGGGGNG is another case

So you the prob as
7 (.7)^(.3)
= appr .247

or

C(7,1) (.7)^6 (.3) = appr .247