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. (i) What is the probability that a hurricane will occur in the eastern Gulf of Mexico and strike Florida this year? (ii) 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)?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
. (a) 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
(i) What is the probability that a hurricane will occur in the eastern Gulf of Mexico and strike Florida this year?
(ii) 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)?
(b) A company is considering upgrading its computer system, and a major portion of the upgrade is a new operating system. The company has asked an engineer for an evaluation of the operating system. Suppose the probability of a favorable evaluation is 0.65. If the probability the company will upgrade its system given a favorable evaluation is 0.85, what is the probability that the company will upgrade and receive a favorable evaluation?
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