1. If the occurrences of high winds and earthquakes are unrelated, and if, at a

Question

1. If the occurrences of high winds and earthquakes are unrelated, and if, at a particular location, the probability of a “high” wind occurring throughout any single minute is 10-5 and the probability of a “moderate” earthquake during any single minute is 10-8:

A. Find the probability of the joint occurrence of the two events during any minute. Building codes do not require the engineer to design the building for the combined effects of these loads. Is this reasonable?

B. Find the probability of the occurrence of one or the other or both during any minute. For rare events, ie events with small probabilities of occurrence, the engineer frequently assumes

      P[AB] P[A] + P[B]. Comment.

C. If the events in succeeding minutes are mutually independent, what is the probability that there will be no moderate earthquakes in a year near this location? In 10 years? Approximate answers are acceptable.

Explanation / Answer

A) For unrelated events A and B, the probability of occurance of both, P(A and B) = P(A) x P(B)

= 10-5 x 10-8

= 10-13

B) P(A U B) = P(A) + P(B) - P(A and B)

Here, P(A and B) is a very small value and hence negligible. So, the probability of oocurance of the event can be taken as P(A) + P(B)

= 10-5 + 10-8

= 1001x10-5

C) Number of minutes in a year = 365x24x60 = 5.256x105

P(earthquake in a year) = 5.256x105 x 10-8

= 0.0053

P(there will be no moderate earthquake) = 1 - 0.0053 = 0.9947

Number of minutes in 10 years = 10x365x24x60 = 5.256x106

P(earthquake in 10 years) = 5.256x106 x 10-8

= 0.053

P(there will be no moderate earthquake) = 1 - 0.053 = 0.947

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