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 U A₂) = 0.80, P(A₂n 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 does not like both vehicle #2 and vehicle # 3. O 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(A₂n A3) P(A₂)P(A3). Therefore, and A3 are independent. No. P(A₂ | A3) = P(A₂). Therefore, A₂ and A3 are not independent. # = A₂ 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 four decimal places.)

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

Q: 2. Let A and B be events with P(A) = 0.5 and P(AnB") = 0.4. For what value of P(B) will A and B be…

A:

Q: he events A and B are independent such that P(A) =0.4 and P(A UB)= 0.88. Find P(B)

A: As per bartleby guideline expert have to answer first three subpart only dear student please upload…

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

A:

Q: Suppose that A and B are two events for which P(A)=0.26, P(B)=0.76, and P(B|A)=0.51. Find each of…

A:

Q: Let X and Y be two events such that P(X)=0.5,P(Y)=m, and P(X∪Y)=0.8. Find the value of m for which X…

A:

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…

A:

Q: The P(A)=0.48P(A)=0.48 and the P(B)=0.06P(B)=0.06. Events AA and BB are mutually exclusive. What is…

A: Given, P(A)=0.48 P(B)=0.06 P(A or B)=?

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: let a and b be two events with P(A) = 3/8, P(B) = 3/8, and P(A∩B) = 1/8. the value of P(A U B) is

A: From the provided information, P (A) = 3/8 P (B) = 3/8 P (A ∩ B) = 1/8

Q: Q2. Two events A and B are said to be dependent if and only if:

A: Here use basic of dependent events

Q: Let A and B be events such that P(A) =1/8, P(A or B)=1/6 and P(A and B)=1/11. Determine P(B)

A: P(A) =1/8, P(A or B)=1/6,  P(A and B)=1/11.

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)

A:

Q: and B are events such that P(A)= 2/7 and P (A&B)= 3/25. Determine P (B I A).

A: Given data,P(A)=27P(A & B)=325P(B|A)=?

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)' =?

Q: Consider two events, A and B. Suppose that P(A)=.40,P(B)=.50,  and P(A∩B)=0.2 . Calculate the value…

A:

Q: If P(A) 04, P(B') =05 and P(A and B) 0 01 Which statement is correct? I P(B)= 06 %3D 2 P(A/B) 0 02 3…

A: Note: Hey, since multiple questions are posted, we will answer first question for you. If you want…

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

A: For independent events, the probability of both event occurring is just equal to the product of the…

Q: Let A and B be events with P(4) =0.3, P(B) =0.73, and P(B 4) = 0.9. Find P(A and B). P(4 and B) =

A: Given data:

Q: 3 b. X and Y are two events, P(Y)==, P(X|Y)=, and PYoX 10 %3D %3D Find P(XnY) and P(X).

A: Given P(Y) = 35, P(X/Y) = 23     and   PY ∩ X = 310

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

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(AC or…

A:

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 A and B are independent events with P(A) = .6 and P(B) .8. Find (a) P(AU B), (b) P(AU B“),…

A: Given,P(A)=0.6P(B)=0.8and A, B are independent events

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: Let A and B be events. Assume that P(A) = 0.55, P(B|A) = 0.36, and P(B|A') = 0.84. Then, P(A∩B)=?,…

A: P(A) = 0.55P(B|A) = 0.36P(B|A') = 0.84

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…

A: As given by the question There are given that two events and their values: PA=0.4PB=0.1 From the…

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

A:

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: , determine P(AB).

A: Here given  P(A) =  1/2 P(A - B) = 1/3