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 X = number of dandelions per square meter.
The average number of dandelions per square meter is, λ = 2.
The random variable X follows a Poisson distribution with parameter λ = 2.
The probability mass function of X is:
[tex]P(X=x)=\frac{e^{-2}2^{x}}{x!};\ x=0,1,2,3...[/tex]
(a)
Compute the value of P (X = 0) as follows:
[tex]P(X=0)=\frac{e^{-2}2^{0}}{0!}=\frac{0.13534\times 1}{1}=0.1353[/tex]
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)
[tex]=1-0.1353\\=0.8647[/tex]
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.
