Respuesta :
Answer:
0.1944
Step-by-step explanation:
Given that the number of Bigfoot sightings per year in the Northwestern US (say X) is well-modeled by a Poisson random variable with an average of 3 sightings occurring per year.
[tex]P(X=x) = \frac{e^{-3} *3^x}{x!}\\\[/tex]
the probability that in a given year there are at least 4 sightings in this region, given that there are at least 2 sightings
=Prob that there are atleast 4 sightings/Prob atleast 2 sightings
(since intersection of these two events is atleast 4)
=[tex]\frac{P(X\geq 4 }{P(X\geq 2} \\\\=\frac{0.184737}{0.950213} =0.194416[/tex]
Reqd prob = 0.1944
The probability that in a given year there are at least 4 sightings in this region, given that there are at least 2 sightings is 0.19.
Given
The number of Bigfoot sightings per year in the Northwestern US is well-modeled by a Poisson random variable with an average of 3 sightings occurring per year.
What is probability?
The quality or state of being probable; the extent to which something is likely to happen or be the case:
The probability of getting X successes from a Poisson experiment.
The probability distribution of a Poisson random variable is called a Poisson distribution.
PMF of a Poisson Distribution formula:
[tex]\rm P(X=x)= \dfrac{e^{-\lambda}\lambda^{x}}{x!}\\\\The \ value \ of \ \lambda \ is \ 3.\\\\ P(X=x)= \dfrac{e^{-3} 3^{x}}{x!}\\[/tex]
Therefore,
The probability that in a given year there are at least 4 sightings in this region, given that there are at least 2 sightings is;
[tex]\rm \dfrac{P(X\geq 4)}{P(X\geq 2)} = \dfrac{\dfrac{e^{-3} 3^{4}}{4!}}{\dfrac{e^{-3} 3^{2}}{2!}}\\\\ \dfrac{P(X\geq 4)}{P(X\geq 2)} =\dfrac{0.18}{0.95}\\\\\dfrac{P(X\geq 4)}{P(X\geq 2)} =0.19[/tex]
Hence, the probability that in a given year there are at least 4 sightings in this region, given that there are at least 2 sightings is 0.19.
To know more about Probability click the link given below.
https://brainly.com/question/795909
