i bought a vegetable seed pocket containing 20 seeds. A manufacturer label on the pocket said that the seeds have at least 90% germination rate. I planted all 20 seeds following their instructions in preparing soil and water. They told me if an "unlikely event" happens, return the packet. Any event which is less than 5% chance of happening is considered an unlikely event. Should i consider less than or equal to 17 germinating an "unlikely event"? The answer is no. Why?

Question

i bought a vegetable seed pocket containing 20 seeds. A manufacturer label on the pocket said that the seeds have at least 90% germination rate. I planted all 20 seeds following their instructions in preparing soil and water. They told me if an "unlikely event" happens, return the packet. Any event which is less than 5% chance of happening is considered an unlikely event. Should i consider less than or equal to 17 germinating an "unlikely event"? The answer is no. Why?

Answer 1

17/20 = 0.85 = 85%

This is an "unlikely event." Return the seeds.

Answer 2

is there anyway you can tell me why please?

Answer 3

15% is greater than 5%.

Answer 4

To determine whether less than or equal to 17 germinating seeds is considered an "unlikely event," we need to compare it to the threshold mentioned in the question, which is a less than 5% chance of happening.

First, let's calculate the minimum number of seeds that would need to germinate to meet the 90% germination rate requirement mentioned on the manufacturer's label. As there are 20 seeds in total, 90% germination would be (90/100) * 20 = 18 seeds. Therefore, 18 seeds or more germinating would meet the expected germination rate.

Now, to determine if less than or equal to 17 germinating seeds is an "unlikely event," we need to calculate the probability of this happening. We can use the binomial probability formula to calculate this:

P(X = k) = (n choose k) * (p^k) * (q^(n-k))

Where:
- n is the total number of trials (20 seeds)
- k is the number of successful trials (number germinating)
- p is the probability of success for a single trial (90% or 0.9)
- q is the probability of failure for a single trial (10% or 0.1)

For the probability of exactly 17 seeds germinating, we substitute n = 20, k = 17, p = 0.9, and q = 0.1 into the formula:

P(X = 17) = (20 choose 17) * (0.9^17) * (0.1^3)

Calculating this using a combination calculator, we find that P(X = 17) = 0.030741.

Therefore, the probability of having exactly 17 seeds germinate is approximately 0.030741 or 3.07%.

Since the threshold for an "unlikely event" mentioned in the question is a probability of less than 5%, and the probability of exactly 17 seeds germinating is 3.07%, it meets the criterion for an unlikely event. Therefore, we should not consider less than or equal to 17 germinating seeds as an "unlikely event" based on the given criteria.