# It is known that, in a certain area of a large city, the average number of rats per bungalow is five. Assuming that the number of rats follows Poisson distribution, find the probability that a random - Mathematics and Statistics

Sum

It is known that, in a certain area of a large city, the average number of rats per bungalow is five. Assuming that the number of rats follows Poisson distribution, find the probability that a randomly selected bungalow has exactly 5 rats.

#### Solution

Let X denote the number of rats per bunglow.
Given, m = 5 and e–5 = 0.0067
∴ X ~ P(m) ≡ X ~ P(5)
The p.m.f. of X is given by

P(X = x) = ("e"^-"m" "m"^x)/(x!)

∴ P(X = x) = ("e"^-5*(5)^x)/(x!), x = 0, 1, ..., 5

P(exactly five rats)
= P(X = 5)

= ("e"^-5*(5)^5)/(5!)

= (0.0067 xx 5^5)/(5 xx 4 xx 3 xx 2 xx1)

= (0.0067 xx 625)/(24)

= (4.1875)/(24)
= 0.1745

Concept: Poisson Distribution
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Exercise 8.4 | Q 1.07 | Page 152