Question

Let \(A\) denote the event that a building suffers structural damage from earthquake and \(B\) denote the event that a building suffers structural damage from wind. Given \(P(A) = 0.01\) and \(P(B) = 0.001\). Assume the two events are independent and that the building can be damaged only from these two events (the building is fireproof, waterproof, floodproof, corrosion proof etc), calculate the probability of structural damage?

Answer 1

0.01099

Explanation:

We are given that

A=Event that a building suffers structural damage from earthquake

B=Event that a building suffers structural damage from wind

P(A)=0.01

P(B)=0.001

Two events A and B are independent

`P(A\cap B)=P(A)\cdot P(B)`

We have to find the probability of structural damage.

We know that

`P(A\cup B)=P(A)+P(B)-P(A\cap B)`

Substitute the values

`P(A\cup B)=0.01+0.001-0.01(0.001)`

`P(A\cup B)=0.01099`