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Let X be the number of lightning strikes in a year at the top of particular mountain.
X follows Poisson distribution with mean μ = 3.8
We have to find here the probability that in randomly selected year the number of lightning strikes is 0
The Poisson probability is given by,
P(X=k) =
Here we have X=0, mean =3.8
Hence probability that X=0 is given by
P(X=0) =
P(X=0) =
P(X=0) = 0.0224
The probability that in a randomly selected year, the number of lightning strikes is 0 is 0.0224
We are given
we can use distribute property
Distributive property:
so, we can write it as
now, we can multiply terms
and we get
..............Answer