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The probability of an economic decline in a certain year is 0.21. There is a probability of 0.61 that we will elect a republican president in the same year. If we elect a republican president, there is a 0.34 probability of an economic decline. Let D represent the event of an economic decline and R represent the event of election of a Republican president. (a) Are R and D independent events? O Yes, because P(D) * P(D|R). O Yes, because P(D) = P(D|IR). O No, because P(D) + P(DIR). O No, because P(D) = P(D|R). (b) What is the probability of a Republican president and economic decline in the year? (c) If we experience an economic decline in the year, what is the probability that there will a Republican president? (Round your answer to four decimal places.) (d) What is the probability of economic decline or a Republican president in the year? Hint: You want to find P(D U R).

The probability of an economic decline in a certain year is 0.21. There is a probability of 0.61 that we will elect a republican president in the same year. If we elect a republican president, there is a 0.34 probability of an economic decline. Let D represent the event of an economic decline and R represent the event of election of a Republican president. (a) Are R and D independent events? O Yes, because P(D) * P(D|R). O Yes, because P(D) = P(D|IR). O No, because P(D) + P(DIR). O No, because P(D) = P(D|R). (b) What is the probability of a Republican president and economic decline in the year? (c) If we experience an economic decline in the year, what is the probability that there will a Republican president? (Round your answer to four decimal places.) (d) What is the probability of economic decline or a Republican president in the year? Hint: You want to find P(D U R).

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
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The probability of an economic decline in a certain year is 0.21. There is a probability of 0.61 that we will elect a republican president in the same year. If we elect a republican president, there is a 0.34 probability of an economic decline. Let D represent the event of an economic decline and R represent the event of election of a Republican president. (a) Are R and D independent events? Yes, because P(D) + P(D|R). Yes, because P(D) = P(D|R). No, because P(D) + P(D|R). No, because P(D) = P(D|R). (b) What is the probability of a Republican president and economic decline in the year? (c) If we experience an economic decline in the year, what is the probability that there will a Republican president? (Round your answer to four decimal places.) (d) What is the probability of economic decline or a Republican president in the year? Hint: You want to find P(D U R). O O O O
Transcribed Image Text:The probability of an economic decline in a certain year is 0.21. There is a probability of 0.61 that we will elect a republican president in the same year. If we elect a republican president, there is a 0.34 probability of an economic decline. Let D represent the event of an economic decline and R represent the event of election of a Republican president. (a) Are R and D independent events? Yes, because P(D) + P(D|R). Yes, because P(D) = P(D|R). No, because P(D) + P(D|R). No, because P(D) = P(D|R). (b) What is the probability of a Republican president and economic decline in the year? (c) If we experience an economic decline in the year, what is the probability that there will a Republican president? (Round your answer to four decimal places.) (d) What is the probability of economic decline or a Republican president in the year? Hint: You want to find P(D U R). O O O O
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