There are seven geologic faults (and possibly more) capable of generating a magnitude 6.7 earthquake in the region around San Francisco. Their probabilities of rupturing by the year 2032 are 27%, 21%, 11%, 10%, 4%, 3%, and 3% (a) Calculate the probability that at least one of these faults erupts by the year 2032, assuming that these are indepen-dent events. (b) Scientists forecast a 62% chance of an earthquake with magnitude at least 6.7 in the region around San Francisco by the year 2032. Compare this with your answer from part (a). Consider the realism of the assumption of inde-pendence. Also consider the role of roundoff. For example, the probability of 10% for one of the faults is presumably rounded to the nearest percent, with the actual probability between 9.5% and 10.5%

There are seven geologic faults (and possibly more) capable of generating a magnitude 6.7 earthquake in the region around San Francisco. Their probabilities of rupturing by the year 2032 are 27%, 21%, 11%, 10%, 4%, 3%, and 3% (a) Calculate the probability that at least one of these faults erupts by the year 2032, assuming that these are indepen-dent events. (b) Scientists forecast a 62% chance of an earthquake with magnitude at least 6.7 in the region around San Francisco by the year 2032. Compare this with your answer from part (a). Consider the realism of the assumption of inde-pendence. Also consider the role of roundoff. For example, the probability of 10% for one of the faults is presumably rounded to the nearest percent, with the actual probability between 9.5% and 10.5%

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Based on data from a statistical abstract, only about 15% of senior citizens (65 years old or older) get the flu each year. However, about 31% of the people under 65 years old get the flu each year. In the general population, there are 14.5%senior citizens (65 years old or older). (Round your answers to three decimal places.) (a) What is the probability that a person selected at random from the general population is senior citizen who will get the flu this season?
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There are seven geologic faults (and possiblymore) capable of generating a magnitude 6.7 earthquake in theregion around San Francisco. Their probabilities of rupturingby the year 2032 are 27%, 21%, 11%, 10%, 4%, 3%, and 3%.Source: Science News.a. Calculate the probability that at least one of these faults erupts by the year 2032, assuming that these are indepen-dent events. b. Scientists forecast a 62% chance of an earthquake withmagnitude at least 6.7 in the region around San Franciscoby the year 2032. Compare this with your answer from parta. Consider the realism of the assumption of independence. Also consider the role of roundoff. For example, the prob-ability of 10% for one of the faults is presumably rounded to the nearest percent, with the actual probability between9.5% and 10.5%.
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