The prior probabilities for events A₁, A₂, and A3 are P(A₂) = 0.20, P(A₂) = 0.50, and P(A3) = 0.30. The conditional probabilities of event B given A₁, A₂, and A3 are P(B | A₁) = 0.30, P(B|A₂) = 0.50, and P(B | A₂) = 0.20. (Assume that A₁, A₂, and A are mutually exclusive events whose union is the entire sample space.) (a) Compute P(B n A₂), P(B n A₂), and P(B n A3). x P(BnA₂) = P(Bn A₂) = X P(Bn A₂) x P(A)P(BIA) (b) Apply Bayes' theorem, PA, 1 B) = P(A₁)P(B | A₁) + P(A₂)P(B | A₂) + ... + P(A)P(B \ A₂)” A₁ - A₂ (c) Use the tabular approach to applying Bayes' theorem to compute P(A₁ | B), P(A₂ 1 B), and P(A3 | B). (Round your answers to two decimal places.) Events P(A₁) P(BA) P(A,B) P(A, IB) A3 X 0.20 0.50 0.30 1.00 0.30 0.50 C C 0.20 . CHEL SAN to compute the posterior probability P(A₂ | B). (Round your answer to two decimal places.) 1.00

Q: are events A and B independent?

A: For the events to be independent, we must have P(A and B) = P(A).P(B)

Q: P(A)=0.56,P(B)=0.54,P(B∪A)=0.91P(A)=0.56,P(B)=0.54,P(B∪A)=0.91 Find the following probabilities.…

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Q: Suppose A and B are events with P(A) = 0.3, P(B) = 0.85, and P(B|A) = 0.6. Find the value of P(A or…

A: given data  P(A) = 0.3 P(B) = 0.85 P(B|A) = 0.6 P(A or B) = ?

Q: Given that P(A) = 0.42, P(B) = 0.04, and P(A and B) = 0.0168, are events A and B independent?

A: It is given that P(A)=0.42, P(B)=0.04, and P(A and B)=0.0168.

Q: =. Compute P(Β n Α1) , P(Β n A2), and Ρ(BnA:). P(Βη Αι) = P(Bn A2) = P(Β η As) =| b. Apply Bayes'…

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Q: If A and B are independent events, P(A)=0.25, and P(B)=0.79, what is P(B|A)?

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Q: Prior Probabilities for A1 and A2: P(A1)=0.20, P(A2)=0.40, (A1) and (A2) are mutually exlcusive.…

A: Data given P(A1)=0.20, P(A2)=0.40, (B|A1)=0.20, P(B|A2)=0.05

Q: Given P(A) = 0.67, P(B) = 0.70, and the fact that events A and B are independent, What is P(A and…

A: GivenP(A)=0.67P(B)=0.70The events A and B are independent

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: P(A)=0.56,P(B)=0.52,P(B∩A¯¯¯¯)=0.32P(A)=0.56,P(B)=0.52,P(B∩A¯)=0.32 Find the following…

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Q: If P(E∩F)=0.035, P(E|F)=0.14, and P(F|E)=0.2, then (a)   P(E)= (b)   P(F)= (c)   P(E∪F)= (d) Are the…

A: Given information: P(E∩F)=0.035, P(E|F)=0.14, and P(F|E)=0.2. (a)  PF|E=PE∩FPE      0.2  =0.035PE…

Q: If A and B are independent events, P(A)=0.22, and P(B)=0.71, what is P(B|A)?

A: Given: A and B are independent P(A)=0.22 P(B)=0.71   A and B are independent means that occurring of…

Q: Events A and B are mutually exclusive with P(A) equal to 0.331 and P (A or B) equal to 0.727. Find…

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Q: P(A) = 0.61, P(B) = 0.67, P(BU A) = 0.91 Find the following probabilities. P(AN B) = P(B|A) = P(A|B)…

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Q: Given P(A) = 0.03, P(B) = 0.42, and P(A or B) = 0.11, are events A and B mutually exclusive?

A: Given: P(A) = 0.03 P(B) = 0.42 P(A or B) = 0.11 Objective of the question is to find if A and B are…

Q: Suppose P(A) = 0.2, P(B) - 0.45, and P(A n B) = 0.02. Find the following probabilities. P(A n B) =…

A: Given that, P(A) =0.2P(B) = 0.45P(A∩B)=0.02

Q: Given that P(A) = 0.09 P(B) = 0.20 and P(A and d B)=0.018 , are events A and independent ?

A: Given: P(A) = 0.09 P(B) = 0.20 P(A and B)=0.018 The objective is to find if events A and B are…

Q: Given P(A) = 0.86, P(B) = 0.08, and the fact that events A and B are independent, What is P(A and…

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Q: P(A)=0.64,P(B)=0.45,P(B∪A)=0.92 Find the following probabilities. P(A∩B) =  P(B|A¯) =  P(A¯|B) =

A: We have given that,  P(A)=0.64, P(B)=0.45, P(B∪A) or P(AUB) =0.92 Then,  We will find the following…

Q: Given P(A) = 0.32, P(B) = 0.44, and the fact that events A and B are independent, What is P(A and…

A: Solution: From the given information, P (A) = 0.32, P (B) = 0.44.

Q: Given P(A) = 0.59, P(B) = 0.51, P(C) = 0.09 and that events A, B, and C are independent, what is…

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Q: Suppose that A, B are two independent events, with P(A) = .1 and P(B) = .2. Find P(A|B).

A:

Q: If A and B are independent events with P(A) = 0.25 and P(B) = 0.60,then P(A|B) is?

A: Given: A and B are independent events. P(A)=0.25P(B)=0.6 The objective is to find P(AB).

Q: Given P(A)=0.31, P(B)=0.49 and P(A or B)=0.78, are events A and B mutually exclusive

A: According to the given information, we have P(A) = 0.31 P(B) = 0.49 P(A or B) = 0.78

Q: Given P(A) = 0.34, P(B) = 0.60, and P(A or B) = 0.24, are events A and B mutually exclusive? %3D %3D…

A: From the provided information, P (A) = 0.34 P (B) = 0.60 P (A or B) = 0.24 Two events A and B are…

Q: Suppose that P(A)= 0.6 and P(B)= 0.5. If events A and B are independent, find the probabilities:…

A:

Q: U and V are mutually exclusive events. P(U) = 0.16; P(V) = 0.6. Find:  a.  P(U and V) =  b.…

A: When A and B are mutually exclusive events,  then  P(A∩B)= 0 P(AUB)=P(A or B) = P(A)+ P(B)-…

Q: U and V are mutually exclusive events. P(U) = 0.28; P(V) = 0.59. Find: a. P(U and V) = b.…

A: Solution: Given Information; Let U and V are mutually exclusive events. P(U)= 0.28 P(V)=0.59

Q: U and V are mutually exclusive events. P(U) = 0.33; P(V) = 0.5. Find:  a.  P(U and V) =  b.…

A: Therefore,

Q: Find P(A or B or C) for the given probabilities. P(A) = 0.33, P(B) = 0.24, P(C)= 0.19 P(A and B) =…

A:

Q: P(A) = 0.6 P(B) = 0.5 P(A|B) = 0.42 P(A) = 0.3 P(B) = 0.5 P(A|B) = 0.3 P(A) = 0.45 P(B) = 0.75 P(A…

A: Determine if events A and B are independent for given problems

Q: Given P(A and B) = 0.43, P(A) = 0.81, and P(B) = 0.25 are events A and B independent or dependent?

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Q: Suppose that E and F are two events and that P(E and F)=0.48, P(F)=0.55, and P(E)=0.5. What is P(F…

A: Suppose that E and F are two events and that P(E and F)= 0.48 P(F)=0.55 and P(E)=0.5 What is P(F |E)…