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Question 4 Suppose that P(BA) = and that P(B|A2 , where A1 and Az are two...
Question 3 Let A, and Az be two events such that P (A1) = 1/4, P (A1A2) = 3/16, and P (AZ I A1 = 1/8. Calculate P (A). a 32 b. od to Moving to the next question prevents changes to this answer
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...
The prior probabilities for events A1 and A2 are P(A1) = .50 and P(A2) = .50. It is also known that P(A1 A2) = 0. Suppose P(B | A1) = .10 and P(B | A2) = .04. Are events A1 and A2 mutually exclusive? Compute P(A1 B) (to 4 decimals). Compute P(A2 B) (to 4 decimals). Compute P(B) (to 4 decimals). Apply Bayes' theorem to compute P(A1 | B) (to 4 decimals). Also apply Bayes' theorem to compute P(A2 |...
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(6) Suppose that PCB An) = – and that P(B A2) = where Aq and A2 are two equiprobable events forming a partition of 12. Calculate P(AB).
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).
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...
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 ∩...
1. Prove“inclusion-exclusion,”thatP(A∪B)=P(A)+P(B)−P(A∩B). 2. Prove the “unionbound, ”thatP(A1∪A2)≤P(A1)+P(A2). Under what conditions does the equality hold? 3. Provethat, for A1 andA2 disjoint, P(A1∪A2|B)=P(A1|B)+P(A2|B). 4. A and B are independent events with nonzero probability. Prove whether or not A and Bc are independent.
6) (10 points) The prior probabilities for events A1 and A2 are P(A1) = 0.40 and P(A2) = 0.60. It is also known that P(A1 or A2) = 1. Suppose P(BA1) = 20 and P(B|A2) =0.05. a. Are A1 and A2 mutually exclusive? Explain. (2 point) b. What is the probability that A1 does not occur? (2 point) C. Compute P(A2 and B) if A1 and B are independent (3 points) d. Compute P(A1 and B) (3 points)
Suppose that A1,A2,.., Ak are mutually exclusive events and P(B)>0. Prove that