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

To determine whether less than or equal to 17 germinating seeds is considered an "unlikely event," we need to understand the concept of probability and the given information.

The manufacturer label stated that the seeds have at least a 90% germination rate. This means that, on average, at least 90% of the seeds will successfully germinate. Therefore, if we assume that the seeds follow this average germination rate, we would expect at least 18 out of the 20 seeds (90% of 20) to germinate successfully.

Now, the manufacturer also mentions that any event with a less than 5% chance of happening is considered "unlikely." In this case, we can calculate the probability of having less than or equal to 17 seeds germinate.

First, we calculate the probability of having exactly 17 seeds germinate. Since each seed has a 90% chance of germination, the probability that a specific seed does not germinate is 10% or 0.1. Therefore, the probability that exactly 17 seeds germinate and 3 do not can be calculated using the binomial probability formula:

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

Using the binomial coefficient notation (20 choose 17) = 20! / (17! * 3!), which is equal to 1140, the calculation becomes:

P(17 germinate) = 1140 * (0.9)^17 * (0.1)^3

Similarly, we can calculate the probability for 16, 15, 14, and so on, germinating seeds.

To determine the total probability of having less than or equal to 17 seeds germinate, we need to sum all these individual probabilities:

P(less than or equal to 17 germinate) = P(17 germinate) + P(16 germinate) + P(15 germinate) + ... + P(1 germinate) + P(0 germinate)

After calculating this sum, we can then compare it to the 5% threshold to determine if it falls under the category of an "unlikely event."

However, since the given information does not provide the exact germination probability for each seed, we cannot calculate the actual probability. Therefore, without this specific data, we cannot determine if less than or equal to 17 germinating seeds will be considered an "unlikely event."