The damage in a structure after an earthquake can be classified as either none, light, or heavy. For a new undamaged structure, the probabilities that it will suffer light and heavy damages after an earthquake are 2.5% and 1%, respectively. However, for an old structure with light damage from a previous earthquake, its probability of getting heavy damage during the next earthquake is 60%. (a) For a new structure, what is the probability that it will be heavily damaged after two earthquakes? Assume no repairs were done after the first earthquake. (b) If the structure is heavily damaged after two earthquakes, what is the probability that the structure was either undamaged or with light damage before the second earthquake?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The damage in a structure after an earthquake can be classified as either none, light, or heavy. For a new undamaged structure, the probabilities that it will suffer light and heavy damages after an earthquake are 2.5% and 1%, respectively. However, for an old structure with light damage from a previous earthquake, its
(a) For a new structure, what is the probability that it will be heavily damaged after two earthquakes? Assume no repairs were done after the first earthquake.
(b) If the structure is heavily damaged after two earthquakes, what is the probability that the structure was either undamaged or with light damage before the second earthquake?
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