Question

. During a year, the probability a structure will be damaged by an earthquake (A) is 0.02, that it will be damaged by a hurricane (B) is 0.03, and that it will be damaged by both is 0.007. What is the probability that it will not be damaged by a hurricane or an earthquake during that year?

Answer 1

0.9506

Explanation:

Pr(A) = 0.02

Pr(B) = 0.03

Pr(both) = 0.007

So,

Pr(Not A) = 1 - Pr(A)

= 1 - 0.02

= 0.98

Pr(Not B) = 1 - Pr(B)

= 1 - 0.03

= 0.97

Pr(Not by both) = 1 - Pr(both)

= 1 - 0.007

= 0.993

Thus,

Pr(Not B) or Pr(Not A) = 0.97 × 0.98

= 0.9056

∴ the probability that the house would not be damaged by a hurricane or an earthquake during the year is 0.9506.