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The San Francisco Bay Area is near several geological fault lines and is therefore vulnerable to the constant threat of earthquakes. According to a study by the U.S. Geological Survey, the probability of a magnitude 6.7 or greater earthquake in the Greater Bay Area in the next 30 years is 0.63. The probability of a large earthquake within the next 30 years along four major fault lines is given in the following table.

1525_Tab 02.jpg

Suppose earthquakes occur in this area independently of one another.

a. What is the probability that there will be a major earthquake within the next 30 years in all four fault regions? Write a Solution Trail for this problem.

b. What is the probability that there will be no major earthquake within the next 30 years in any of the four regions?

c. What is the probability that there will be a major earthquake within the next 30 years in at least one of the four regions?

d. Suppose each probability is doubled if we consider the next 40 years. What is the probability that there will be a major earthquake within the next 40 years in at least one of the four regions?

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