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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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%.
Seventy-seven percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 62% have an emergency locator, whereas 89% of the aircraft not discovered do not have such a locator. Suppose a light aircraft has disappeared. (Round your answers to three decimal places.) (a) If it has an emergency locator, what is the probability that it will not be discovered? (b) If it does not have an emergency locator, what is the probability that it will be discovered?
Let's say that on the Island of Sodor, it rains 15% of the time, and due to the frequent shifts in the wind, no weather today seems to have any impact on weather tomorrow. If we go outside for a week, what is the probability that we observe rain not at all exactly once twice thrice four times five times six times seven times.
An aircraft seam requires 26 rivets. The seam will have to be reworked if any of these rivets is defective. Suppose rivets are defective independently of one another, each with the same probability. (Round your answers to four decimal places.) (a) If 24% of all seams need reworking, what is the probability that a rivet is defective? 0.010 X (b) How small should the probability of a defective rivet be to ensure that only 5% of all seams need reworking?
Historical climate records indicate that the probability of there being more than 100 cm of snow on the ground at Winnipeg airport on January 15 is .60 (three in five). What is the probability that over the next five years: (a) snow depth is never more than 100 cm on January 15? (b) in four or more of the years, there is more than 100 cm of snow on January 15?
Question 2 (a) One of the famous fast-food chains in Malaysia has a brand name recognition rate of 95% around the world. If we randomly select 16 people, (i) compute the probability that exactly 13 people recognize the brand. (ii) compute the probability that between 5 and 12 people do not recognize the brand.
Based on data from a statistical abstract, only about 13% of senior citizens (65 years old or older) get the flu each year. However, about 30% of the people under 65 years old get the flu each year. In the general population, there are 10% 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? (b) What is the probability that a person selected at random from the general population is a person under age 65 who will get the flu this year? (c) Repeat parts (a) and (b) for a community that has 91% senior citizens and repeat parts (a) and (b) for a community that has 49% senior citizens. please explain the symbols, that is what is keeping me from successfully learning this
Based on data from a statistical abstract, only about 10% of senior citizens (65 years old or older) get the flu each year. However, about 26% 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?(b) What is the probability that a person selected at random from the general population is a person under age 65 who will get the flu this year?(c) Repeat parts (a) and (b) for a community that has 88% senior citizens. (a) (b) (d) Repeat parts (a) and (b) for a community that has 47% senior citizens. (a) (b)
During a year ending April 30 of that year, there were approximately 5.0 million sales of existing homes in the United States, of which 1.1 million were sold in the West. During April of that year there were a total of 410,000 existing homes sold in the United States, of which 130,000 were sold in the West. (Round your answers to two decimal places.) (a) Find the probability that a home sale in the year ending April 30 of that year, took place in the West, given that the home was sold during April of that year. (b) Find the probability that a home sale in the year ending April 30 of that year, took place in April of that year, given that it took place in the West.
At the Bank of California, past data show that 6% of all credit card holders default at some time in their lives. On one recent day, this bank issued 15 credit cards to new customers. Find the probability that of these 15 customers, eventually a. exactly 3 will default Round your answer to four decimal places. P(exactly 3) = i b. exactly 1 will default Round your answer to four decimal places. P(exactly 1) = i c. none will default Round your answer to four decimal places. P( none )= i