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Consider randomly selecting a single individual and having that person test drive 3 different vehicles. Define events A₁, A₂, and A3 by A₁ A₂ = likes vehicle #2 A3 = likes vehicle #3. = likes vehicle #1 Suppose that P(A₁) = 0.45, P(A₂) = 0.55, P(A3) = 0.70, P(A₁ U A₂) = 0.80, P(A₂ A3) = 0.50, and P(A₁ U A₂ U A3) = 0.88. (a) What is the probability that the individual likes both vehicle #1 and vehicle #2? 0.2 (b) Determine P(A₂ | A3). (Round your answer to four decimal places.) P(A₂ | A3) Interpret P(A₂ | A3). If a person likes vehicle #2, this is the probability he or she will also like vehicle #3. = 0.7143 This is the probability a person does not like both vehicle #2 and vehicle #3. If a person likes vehicle #3, this is the probability he or she will also like vehicle #2. This is the probability a person likes both vehicle #2 and vehicle #3. (c) Are A₂ and A3 independent events? Answer in two different ways. (Select all that apply.) Yes. P(A₂ | A3) # P(A₂). Therefore, A₂ and A3 are independent. No. P(A₂ | A3) # P(A₂). Therefore A₂ and A3 are not independent. Yes. P(A₂ A3) = P(A₂)P(A3). Therefore, A₂ and A3 are independent. No. P(A₂ | A3) = P(A₂). Therefore, A₂ and A3 are not independent. Yes. P(A₂ | A3) = P(A₂). Therefore, A₂ and A3 are independent. No. P(A₂ A3) # P(A₂)P(A3). Therefore, A₂ and A3 are not independent. (d) If you learn that the individual did not like vehicle #1, what now is the probability that he/she liked at least one of the other two vehicles? (Round your answer to four decimal places.) 0.56 X

Consider randomly selecting a single individual and having that person test drive 3 different vehicles. Define events A₁, A₂, and A3 by A₁ A₂ = likes vehicle #2 A3 = likes vehicle #3. = likes vehicle #1 Suppose that P(A₁) = 0.45, P(A₂) = 0.55, P(A3) = 0.70, P(A₁ U A₂) = 0.80, P(A₂ A3) = 0.50, and P(A₁ U A₂ U A3) = 0.88. (a) What is the probability that the individual likes both vehicle #1 and vehicle #2? 0.2 (b) Determine P(A₂ | A3). (Round your answer to four decimal places.) P(A₂ | A3) Interpret P(A₂ | A3). If a person likes vehicle #2, this is the probability he or she will also like vehicle #3. = 0.7143 This is the probability a person does not like both vehicle #2 and vehicle #3. If a person likes vehicle #3, this is the probability he or she will also like vehicle #2. This is the probability a person likes both vehicle #2 and vehicle #3. (c) Are A₂ and A3 independent events? Answer in two different ways. (Select all that apply.) Yes. P(A₂ | A3) # P(A₂). Therefore, A₂ and A3 are independent. No. P(A₂ | A3) # P(A₂). Therefore A₂ and A3 are not independent. Yes. P(A₂ A3) = P(A₂)P(A3). Therefore, A₂ and A3 are independent. No. P(A₂ | A3) = P(A₂). Therefore, A₂ and A3 are not independent. Yes. P(A₂ | A3) = P(A₂). Therefore, A₂ and A3 are independent. No. P(A₂ A3) # P(A₂)P(A3). Therefore, A₂ and A3 are not independent. (d) If you learn that the individual did not like vehicle #1, what now is the probability that he/she liked at least one of the other two vehicles? (Round your answer to four decimal places.) 0.56 X

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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Consider randomly selecting a single individual and having that person test drive 3 different vehicles. Define events A₁, A₂, and A3 by A₁ = likes vehicle #1 A₂ A3 = likes vehicle #2 = likes vehicle #3. Suppose that P(A₁) = 0.45, P(A₂) = 0.55, P(A3) = 0.70, P(A₁ U A₂) = 0.80, P(A₂ n A3) = 0.50, and P(A₁ U A₂ U A3) = 0.88. (a) What is the probability that the individual likes both vehicle #1 and vehicle #2? 0.2 (b) Determine P(A₂ | A3). (Round your answer to four decimal places.) P(A₂ | A3) = 0.7143 Interpret P(A₂ | A3). If a person likes vehicle #2, this is the probability he or she will also like vehicle #3. This is the probability a person does not like both vehicle #2 and vehicle #3. If a person likes vehicle #3, this is the probability he or she will also like vehicle #2. This is the probability a person likes both vehicle #2 and vehicle #3. (c) Are A₂ and A3 independent events? Answer in two different ways. (Select all that apply.) # Yes. P(A₂ | A3) + P(A₂). Therefore, A₂ and A3 are independent. No. P(A₂ A3) + P(A₂). Therefore A₂ and A3 are not independent. n = Yes. P(A₂ A3) = P(A₂)P(A3). Therefore, A₂ and A3 are independent. No. P(A₂ | A3) P(A₂). Therefore, A₂ and A3 are not independent. Yes. P(A₂ | A3) = P(A₂). Therefore, A₂ and A3 are independent. No. P(A₂ A3) # P(A₂)P(A3). Therefore, A₂ and A3 are not independent. 0 (d) If you learn that the individual did not like vehicle #1, what now is the probability that he/she liked at least one of the other two vehicles? (Round your answer to four decimal places.) 0.56 X
Transcribed Image Text:Consider randomly selecting a single individual and having that person test drive 3 different vehicles. Define events A₁, A₂, and A3 by A₁ = likes vehicle #1 A₂ A3 = likes vehicle #2 = likes vehicle #3. Suppose that P(A₁) = 0.45, P(A₂) = 0.55, P(A3) = 0.70, P(A₁ U A₂) = 0.80, P(A₂ n A3) = 0.50, and P(A₁ U A₂ U A3) = 0.88. (a) What is the probability that the individual likes both vehicle #1 and vehicle #2? 0.2 (b) Determine P(A₂ | A3). (Round your answer to four decimal places.) P(A₂ | A3) = 0.7143 Interpret P(A₂ | A3). If a person likes vehicle #2, this is the probability he or she will also like vehicle #3. This is the probability a person does not like both vehicle #2 and vehicle #3. If a person likes vehicle #3, this is the probability he or she will also like vehicle #2. This is the probability a person likes both vehicle #2 and vehicle #3. (c) Are A₂ and A3 independent events? Answer in two different ways. (Select all that apply.) # Yes. P(A₂ | A3) + P(A₂). Therefore, A₂ and A3 are independent. No. P(A₂ A3) + P(A₂). Therefore A₂ and A3 are not independent. n = Yes. P(A₂ A3) = P(A₂)P(A3). Therefore, A₂ and A3 are independent. No. P(A₂ | A3) P(A₂). Therefore, A₂ and A3 are not independent. Yes. P(A₂ | A3) = P(A₂). Therefore, A₂ and A3 are independent. No. P(A₂ A3) # P(A₂)P(A3). Therefore, A₂ and A3 are not independent. 0 (d) If you learn that the individual did not like vehicle #1, what now is the probability that he/she liked at least one of the other two vehicles? (Round your answer to four decimal places.) 0.56 X
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