Question

In Islamabad city the mean number of power outages is 4 per month. Find the
probability that in a given month,
a. There are exactly 3 outages
b. There are more than 2 outages.

Answer 1

If your question has an average probability of an event happening per unit (i.e. per unit of time, cycle, event) and you want to find probability of a certain number of events happening in a period of time (or number of events), then use the Poisson Distribution

so x is the random variable that follows Poisson distribution

Given : $\mu =4$

formula: $P(X=x) = e^{-\mu } \mu ^{x}/x!$

a) To find : P(X=3)

P(X=3)= $e^{-4 }(4 ^{3})/3!$ =0.1954

To find $P(X>2)=1-P(x\leq 2)$

=1-[P(x=0)+P(x=1)+P(X=2)]

=1-(0.01832+0.07326+0.14653)

=0.76190