Answer:
(a) The probability that there are no dandelions in a randomly selected area of 1 square meter in this region is 0.1353.
(b) The probability that there are at least one dandelion in a randomly selected area of 1 square meter in this region is 0.8647.
Step-by-step explanation:
Let <em>X</em> = number of dandelions per square meter.
The average number of dandelions per square meter is, <em>λ</em> = 2.
The random variable <em>X</em> follows a Poisson distribution with parameter <em>λ</em> = 2.
The probability mass function of <em>X</em> is:
(a)
Compute the value of P (X = 0) as follows:
Thus, the probability that there are no dandelions in a randomly selected area of 1 square meter in this region is 0.1353.
(b)
Compute the value of P (X ≥ 1) as follows:
P (X ≥ 1) = 1 - P (X < 1)
= 1 - P (X = 0)
Thus, the probability that there are at least one dandelion in a randomly selected area of 1 square meter in this region is 0.8647.