Question 1209744
You're on the right track using the Poisson distribution! Here's how to calculate the probabilities:

**1. Probability of no dandelions:**

* The Poisson distribution formula is: P(x) = (e^-μ * μ^x) / x!
    * Where:
        * P(x) is the probability of x events occurring
        * e is the base of the natural logarithm (~2.71828)
        * μ is the mean number of events (9.9 dandelions per square meter)
        * x is the number of events we're interested in (0 dandelions)
        * x! is the factorial of x (0! = 1)

* Plugging in the values: P(0) = (e^-9.9 * 9.9^0) / 1 
* Calculating this gives you approximately 0.0000504

**2. Probability of at least one dandelion:**

* This is the complement of having no dandelions. So:
* P(at least one) = 1 - P(0) 
* P(at least one) = 1 - 0.0000504 
* P(at least one) ≈ 0.9999496 (which rounds to 0.99995 as you correctly stated)

**3. Probability of at most two dandelions:**

* This means we want the probability of having 0, 1, or 2 dandelions. We need to calculate each of these probabilities and add them together:
    * P(0) = 0.0000504 (calculated above)
    * P(1) = (e^-9.9 * 9.9^1) / 1! ≈ 0.0004988
    * P(2) = (e^-9.9 * 9.9^2) / 2! ≈ 0.002469
* P(at most two) = P(0) + P(1) + P(2)
* P(at most two) ≈ 0.0000504 + 0.0004988 + 0.002469
* P(at most two) ≈ 0.0030182

**Therefore, the probability of at most two dandelions in an area of 1 m² is approximately 0.0030182**