A building is being designed against wind load and earthquakes. During the next

Question

A building is being designed against wind load and earthquakes. During the next 50 years the probability that the building will be damaged only by earthquakes is 0.1, only by wind- storms is 0.05,and by both earthquakes and windstorms is 0.2. Past records show that the in the next 50 years, the probability of occurence of earthquakes and windstorms are 0.1 and 0.6 respectively. Assume independence of earthquake and windstorm occurence. As- sume that there are no other causes of building damage other than earthquakes and wind loads. Determine the probability that the building will be damaged during its service life of 50 years? Hint: Consider the four cases: (i) earthquake only and no windstorm,ii) windstorm only and no earthquake, (iii) earthquake and windstorm, (iv) no earthquake and no windstorm.

Explanation / Answer

Probability that the building will be damaged during its service life = P(earthquake damage) + P(windstorm damage) + P(earthquake and windstorm damage)

Since the events are independent, P(earthquake and windstorm) = 0.1x0.6 = 0.06

P(only earthquake damage) = (P(earthquake) - P(earthquake and windstorm)) x 0.1

= (0.1 - 0.06) x 0.1

= 0.004

P(only windstorm damage) = (P(windstorm) - P(earthquake and windstorm) x 0.05

= (0.6 - 0.06)x0.05

= 0.027

P(earthquake and windstorm damage) = 0.06x0.2 = 0.012

P(building will be damaged in its service life) = 0.004 + 0.027 + 0.012

= 0.043

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