After a large scale earthquake it is predicted that 30% of all buildings have be

Question

  After a large scale earthquake it is predicted that 30% of all buildings have been structurally compromised.

What is the probability that if engineers inspect 10 buildings they will find exactly one that is structurally compromised?
What is the probability that if engineers inspect 10 buildings they will find less than or equal to 2 that are structurally compromised?
What is the probability that if engineers inspect 10 buildings they will find greater than 4 that are structurally compromised?
What is the expected number of buildings that an engineer will find structurally compromised if the engineer inspects 10 buildings?

Explanation / Answer

p=0.30

X no of building structurally comprised is binomial with (10, 0.3)

probability that if engineers inspect 10 buildings they will find exactly one that is structurally compromised

P(x=1)=0.1211

the probability that if engineers inspect 10 buildings they will find less than or equal to 2 that are structurally compromised

=P(X<=2) = 0.3828

probability that if engineers inspect 10 buildings they will find greater than 4 that are structurally compromised

=P(X>4) = 0.1503

E(X) = np = 10(0.3) =3

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