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 = likes vehicle #2 A3 = likes vehicle #3. Suppose that P(A₁) = 0.45, P(A₂) = 0.55, P(A3) = 0.70, P(A₁ UA₂) = 0.80, P(A₂ A3) = 0.50, and P(A₁ UA₂ U A3) = 0.88. (a) What is the probability that the individual likes both vehicle #1 and vehicle #2? (b) Determine P(A₂ I A3). (Round your answer to four decimal places.) P(A₂ | A3) = Interpret P(A₂ A3). O If a person likes vehicle #2, this is the probability he or she will also like vehicle #3. O This is the probability a person likes both vehicle #2 and vehicle #3. O This is the probability a person does not like both vehicle #2 and vehicle #3. O If a person likes vehicle #3 , this s the probability he or she will also like vehicle #2. (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)P(A3). Therefore, A₂ and A3 are not 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. Yes. P(A₂n A3) = P(A₂)P(A3). Therefore, A₂ and A3 are independent. O No. P(A₂ I A3) + P(A₂). Therefore A₂ and A3 are not independent.

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Q: Events A and B are mutually exclusive with P(A) = 0.35 and P(B) = 0.25. Then, P(B) = P(Bº) = (Enter…

A: GivenA and B are mutually exclusiveP(A)=0.35P(B)=0.25

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Q: (ii) The desks in a certain classroom are produced by three different carpenters A, B and C. A…

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Q: 3. A and B are two events such that P(A) =, P(A|B)= and P(A|B')=;. %3D Show that P(AOB) : 64

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Q: 8. For two independent events A and B, P(A and B) =

A: Events A and B are independent if occurrence of one event doesn't depend on any other event.…

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Q: a. Let A and B be two events such that P(A) = 0.05 and P(A U B) = 0,49. Calculate P(B') if events A…

A: Continue with Simple probability theory...............

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A: Solution

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Q: If A and B are two dependent events, P(A) = 0.60 , P(A and B) = 0.153 then P(B/A)= 0.525 O 0.225 МА…

A: Solution: From the given information, P(A) = 0.60 and P(A and B) = 0.153.

Q: (iii) Given that the events A and B are such that : 3 P(A) = P(AUB)= and P (B) = p. 2' Find the…

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Q: 3.if A and B are two events such that P(AUB) = P(ANB) = and P(A) = 3, then P (B) is equal to a. 1/3…

A: The question is about probability.Given probabilities are as follows :

Q: Suppose that C and D are events such that P(C) = 4/5 and P(C&D) = 3/10. Find P(D| C).

A: The formula for conditional probability is,

Q: If A and B are two events with P(A) = 2/3, P(B) = 1/5, P(A ʼn B) = 1/15 then Find P(ANB)

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Q: We have found that A n B = {E₂}. There are five equally likely simple events, E₁, E₂, E5, so each…

A: There are five equally likely simple events,  so each event has probability .

Q: 8. Two events, A and B, are such that P(A)=.45,P(B) = .65,Pl B)=.25, determine PBN

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Q: Two events, A and B, are such that P(A∪B) = 0.86, P(B) = 0.72 and P(A) = 0.64. Determine (i) P…

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Q: For two events, A and B, we have P(A) = 0.8, P(B) = 0.7, and P(AUB) = 0.9. Then, the value for P(BA)…

A: Given that  P(A) = 0.8, P(B) = 0.7, and P(A U B) = 0.9.

Q: Two events, A and B, are such that P(A∪B) = 0.86, P(B) = 0.72 and P(A) = 0.64. Determine P(AUB)'

A: Given data, P(A∪B) = 0.86 P(B) = 0.72  P(A) = 0.64 P(AUB)' =?

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Q: 0. Let A and B be independent events such that P(A) = p, P(B) = 2p. The largest value of p, for…

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Q: If A and B are two events with P(A) = 2/3, P(B) = 1/5, P(A n B) = 1/15 then Find P(ANB)

A: Answer: From the given data, P(A) = 23 P(B) = 15 P(A∩B) =115

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Q: Let A and B be events such that P (A) = 1/5 P (A & B) = 1/10 and P (A or B) = 1/2 Determine P (B)

A: P(A)=15P(A and B) = 110P(A or B) = 12

Q: Suppose that E and F are two events and that P(E)=0.8 and P(F|E)=0.5. What is P(E and F)​?

A: Given data,  P(E)=0.8  P(F|E)=0.5 P(E and F)​=?

Q: Milan state

A: Here's the step-by-step explanations for each part of the problem to help understand how we arrive…

Q: For two events A and B, P(A) = 0.4 and P(B) 0.1. (a) If A and B are independent, then P(ANB)%3D…

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Q: Let A and B are events of an experiment and P(A) = 1/4, P(AUB) = 1/2 then value of P(B/AC) is

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Q: If A and B are two events such that P (A or B) =2/3, P(A N BC )=1/3 and P(A/B)= 1/6. Find P(B).…

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Q: The PMF of the number of components K of a system that fails is defined by PK (k) = {() (0.2)*(0.8)…

A: Solution-; Let, K=be the number of components of system that fails Given: The pmf of K is,…