question archive If a hurricane forms in the eastern half of the Gulf of Mexico, there is a 76 percent chance that it will strike the western coast of Florida
If a hurricane forms in the eastern half of the Gulf of Mexico, there is a 76 percent chance that it will strike the western coast of Florida
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If a hurricane forms in the eastern half of the Gulf of Mexico, there is a 76 percent chance that it will strike the western coast of Florida. From data gathered over the past 50 years, it has been determined that the probability of a hurricane's occurring in this area in any given year is 0.85.
(a) What is the probability that a hurricane will occur in the eastern Gulf of Mexico and strike Florida this year?
(b) If a hurricane in the eastern Gulf of Mexico is seeded (induced to rain by addition of chemicals from aircraft), its probability of striking Florida's west coast is reduced by one-fourth. If it is decided to seed any hurricane in the eastern gulf, what is the new value for the probability in part (a)?
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Answer:
a. the probability that a hurricane will occur in the eastern Gulf of Mexico and strike Florida this year is just the multiplication of probabilities of two events that a hurricane forms in Gulf of Mexico and it hits Florida
which is = ?0.85×0.76
=0.646∼0.65?
b.If it is decided to seed any hurricane in the eastern gulf, what is the new value for the probability in part (a)
becomes ?0.25×0.646
=0.1615∼0.16
