The damage in a structure due after an earthquake can be classified as none (N),

Question

The damage in a structure due after an earthquake can be classified as none (N), light (L), or heavy (H). For a new undamaged structure, the probability that it will suffer light and heavy damages after an earthquake is 0.2 and 0.05, respectively. However, if the structure was already lightly damaged, its probability of getting heavy damage during the next earthquake is increased to 50%.

a) For a new structure, what is the probability that it will be heavily damaged after two earthquakes? Assume that no repair was performed after the first earthquake.

What is tricking me on this question is that no repair was perfomed. This means that after the first earthquake there is a probability that it already suffered light damage. So then the probability for the first and second earth quack would be different.

b) If a structure is indeed heavily damaged after two earthquakes, what is the probability that the structure was either undamaged or lightly damaged before the second earthquake?

This question is just over my head.....

I would greatly apprciate any help!!! Thanks

Explanation / Answer

a. probability that a new structure is heavily damaged after two earth quakes is

=probability of light damage after first earthquake and heavy damaged after second earthquake

=prob(light damage)+ prob(heavy damage|light damage)

=0.2+0.075 =0.275

b. prob(light or no damage after first earthquake|Heavy damage after second earthquake) = prob(light damage | heavy damage after second earthquake) + prob(no damage | heavy damage after second earthquake)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.