Bayes’ Theorem is an important probability result relating the condition probabilities P(A|B) and P(B|A). Here we...
Bayes’ Theorem is an important probability result relating the condition probabilities P(A|B) and P(B|A). Here we develop the formula.
(a) Let A and B be events. What is the definition of P(A|B)? What is the definition of (B|A)?
(b) Compute P(A|B)·P(B) and P(B|A)·P(A).
(c) Find an expression for P(B|A) in terms of P(A), P(B) and P(A|B).
(d) Suppose P(B) =P(A) and P(A|B) = 0.7, find P(B|A).
Homework Answers
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Bayes’ Theorem is an important probability result relating the
condition probabilities P(A|B) and P(B|A). Here we...
Hi, my answers seemed strange after using Bayes theorem, so I am unsure if I made the right calcu...
hi, my answers seemed strange after using Bayes theorem, so I am
unsure if I made the right calculations. Please show your work so I
can catch my error :)
Extra Credit: ELISA tests are used to screen donated blood for the presence of the AIDS virus. The test actually detects antibodies, substances that the body produces when the virus is present. When antibodies are present, ELISA is positive with probability about 0.997 and negative with probability about 0.003. When...
The prior probabilities for events A1 and A2 are P(A1) = 0.45 and P(A2) = 0.50....
The prior probabilities for events A1 and A2 are P(A1) = 0.45 and P(A2) = 0.50. It is also known that P(A1 ∩ A2) = 0. Suppose P(B | A1) = 0.20 and P(B | A2) = 0.05. If needed, round your answers to three decimal digits. a) Are A1 and A2 mutually exclusive? b) Compute P(A1 ∩ B) and P(A2 ∩ B). c) Compute P(B). d) Apply Bayes’ theorem to compute P(A1 | B) and P(A2 | B).
31. Assume that we have two events, A and B. that are mutually exclusive. Assume further...
31. Assume that we have two events, A and B. that are mutually exclusive. Assume further that we know P(A) 30 and P(B) a. What is P(A n B)? b. What is P(A I B)? c. 40. A student in statistics argues that the concepts of mutually exclusive events and inde- pendent events are really the same, and that if events are mutually exclusive they must be independent. Do you agree with this statement? Use the probability information in this...
What is the correct formula for Bayes' theorem? a) P(XY) = am b) P(XY) = P(xor...
What is the correct formula for Bayes' theorem? a) P(XY) = am b) P(XY) = P(xor PY) c) P(X|Y) = PRAXIS d) P(X\Y) = POUR Submit Answer format: Text unanswered not_submitted #2 From the following new information, given low demand, what is the probability of an improving economy? Improving Economy Not improving economy 0.76 Given high demand 0.5 Given Low demand Points: 5/17 Grade: 29.4% Progress: 29.4% Hide
1. (10 pts) Consider two events, A and B, for which we have the following probabilities....
1. (10 pts) Consider two events, A and B, for which we have the following probabilities. P(A)=0.5 P(B) = 0.2 P(AB) 0.7 A. Find the probability P( AB) B. Find the probability P(AUB)
A1) = 0.20 and P( B AZ) = 0.05. If The prior probabilities for events A1...
A1) = 0.20 and P( B AZ) = 0.05. If The prior probabilities for events A1 and Az are P(A1) = 0.35 and P(A2) = 0.60. It is also known that P(Ain Az) = 0. Suppose P( B needed, round your answers to three decimal digits. (a) Are A1 and Az mutually exclusive? Yes Explain your answer. The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank (b) Compute P(Ain...
e. Application of Bayes: Using Bayes theorem driven in item d, show that in the following problem switching is the bett...
e. Application of Bayes: Using Bayes theorem driven in item d, show that in the following problem switching is the better strategy for the player and makes the probability of wining as 2/3, while not switching gives the probability of wining 1/3. Monty Hall: There are 3 doors 1, 2, 3. Randomly, and equally likely, behind one of the door there is a prize, and other two are empty. The player choose one door. He does not open the door...
Recall Bayes' Rule P(AIB) = P(A)P(B|A) PB) Suppose 1 in 100 birds is a duck. 1...
Recall Bayes' Rule P(AIB) = P(A)P(B|A) PB) Suppose 1 in 100 birds is a duck. 1 in 10 birds walks and talks like a duck (for instance, some geese walk and talk like ducks despite not being ducks) 9 out of 10 ducks walk and talk like a duck (some ducks refuse to conform. Here I am saying that the bird walks and talks like a duck, given that the bird is a duck) The probability that a bird is...
The prior probabilities for events A1 and A2 are P(A1) = 0.30 and P(A2) = 0.40....
The prior probabilities for events A1 and A2 are P(A1) = 0.30 and P(A2) = 0.40. It is also known that P(A1 ∩ A2) = 0. Suppose P(B | A1) = 0.20 and P(B | A2) = 0.05. If needed, round your answers to three decimal digits. (a) Are A1 and A2 mutually exclusive? Explain your answer. The input in the box below will not be graded, but may be reviewed and considered by your instructor. (b) Compute P(A1 ∩...
The prior probabilities for events A1 and A2 are P(A1) = 0.40 and P(A2) = 0.45....
The prior probabilities for events A1 and A2 are P(A1) = 0.40 and P(A2) = 0.45. It is also known that P(A1 ∩ A2) = 0. Suppose P(B | A1) = 0.20 and P(B | A2) = 0.05. If needed, round your answers to three decimal digits. (a) Are A1 and A2 mutually exclusive? - Select your answer -YesNoItem 1 Explain your answer. The input in the box below will not be graded, but may be reviewed and considered by...
hi, my answers seemed strange after using Bayes theorem, so I am
unsure if I made the right calculations. Please show your work so I
can catch my error :)
Extra Credit: ELISA tests are used to screen donated blood for the presence of the AIDS virus. The test actually detects antibodies, substances that the body produces when the virus is present. When antibodies are present, ELISA is positive with probability about 0.997 and negative with probability about 0.003. When...
31. Assume that we have two events, A and B. that are mutually exclusive. Assume further that we know P(A) 30 and P(B) a. What is P(A n B)? b. What is P(A I B)? c. 40. A student in statistics argues that the concepts of mutually exclusive events and inde- pendent events are really the same, and that if events are mutually exclusive they must be independent. Do you agree with this statement? Use the probability information in this...
What is the correct formula for Bayes' theorem? a) P(XY) = am b) P(XY) = P(xor PY) c) P(X|Y) = PRAXIS d) P(X\Y) = POUR Submit Answer format: Text unanswered not_submitted #2 From the following new information, given low demand, what is the probability of an improving economy? Improving Economy Not improving economy 0.76 Given high demand 0.5 Given Low demand Points: 5/17 Grade: 29.4% Progress: 29.4% Hide
1. (10 pts) Consider two events, A and B, for which we have the following probabilities. P(A)=0.5 P(B) = 0.2 P(AB) 0.7 A. Find the probability P( AB) B. Find the probability P(AUB)
A1) = 0.20 and P( B AZ) = 0.05. If The prior probabilities for events A1 and Az are P(A1) = 0.35 and P(A2) = 0.60. It is also known that P(Ain Az) = 0. Suppose P( B needed, round your answers to three decimal digits. (a) Are A1 and Az mutually exclusive? Yes Explain your answer. The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank (b) Compute P(Ain...
e. Application of Bayes: Using Bayes theorem driven in item d, show that in the following problem switching is the better strategy for the player and makes the probability of wining as 2/3, while not switching gives the probability of wining 1/3. Monty Hall: There are 3 doors 1, 2, 3. Randomly, and equally likely, behind one of the door there is a prize, and other two are empty. The player choose one door. He does not open the door...
Recall Bayes' Rule P(AIB) = P(A)P(B|A) PB) Suppose 1 in 100 birds is a duck. 1 in 10 birds walks and talks like a duck (for instance, some geese walk and talk like ducks despite not being ducks) 9 out of 10 ducks walk and talk like a duck (some ducks refuse to conform. Here I am saying that the bird walks and talks like a duck, given that the bird is a duck) The probability that a bird is...
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