Q: (a) Prove that for events A and B, if P(B|A) > P(B) then P(A|B) > P(A).
A: As per our guidelines, we are allowed to answer first question only. Thanks Given Events A and B…
Q: a. Assume that the selections are made with replacement. Are the events independent?
A: here use given contingency table
Q: According to special rule of addition P(A or B) = P(A) + P(B), is true if and only if a.A and B are…
A: We need to find the special rule of addition for which P(A or B) = P(A) + P(B) is true .
Q: If B1, B2, .., B, be a set of exhaustive and mutually exclusive events associated with a random…
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Q: Find P(A and B) if P(A) is 0.3 and the P(B) is 0.4, and events A and B are independent.
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Q: Let A and B be two events such that P(A) = 1/7, P(AUB) =1/2, and P(AB) =1/2 Determine P(B)
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Q: If the knowledge that an event A has occurred implies that a second event B cannot occur, then the…
A: If the knowledge that an event A has occurred implies that a second event B cannot occur, then the…
Q: If A and B are events such that P(A)equals=0.60 and P(A∪B)equals=0.70, find P(B) when (a) A…
A: (a)If events A and B are mutually exclusive events, then, P (A or B) = P(A)+ P(B).Or, P(B) = P (A or…
Q: If two events, Event A with probability P(A) and Event B with probability P(B) are independent, then…
A: Probability is a branch of mathematics which is basically deals with the chances of happening an…
Q: A computer-consulting firm presently has bids out on two projects. Let A= [awarded project 1] and B=…
A: Given: PA=0.75, PB=0.35 and PA∩B=0.2.
Q: If A and B are two mutually exclusive events with P(a) > O and P(b) > 0 then it implies they are…
A: Hello, thanks for your question but according to our policy I am answering the very first question.…
Q: Prove or disprove that for any two events A, and A2, P[A, n A-] 21- PÍAG] – P[A£]
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Q: If A and B are two independent events such that P(AUB) = 0.8, and P(A) 0.3, %3D then Find P(B)?
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Q: If two events are disjoint, can they be independent? If yes, give an example; if no, prove that it…
A: Independent events: Two or more events are said to be independent if the occurrence of one does not…
Q: If A and B are independent events such that P(A) = 0.4 and P %3D
A: Concept: If the probability of occurrence of one event is not affected by the probability of…
Q: Suppose we have three events A, B, and C. If P(A) > 0, P(B) > 0 and P(C) < 1, and we know that if…
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Q: If A, B, C are are independent of C. independent events, show directly that both AUB and A\ B
A: Given that A, B, and C are independent means that, A∩B=B∩C=C∩A=A∩B∩C=φ.... (1) Now, A∪B be can be…
Q: 14. If the outcome of event A is not affected by event B, then events A and B are said to be : A.…
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Q: Consider the problem of selecting two applicants for a job out of a group of five and imagine that…
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Q: Theorem 3.16. For any three events A, B and C, Р (AnB IC)+ P (AnBIC)- Р (AI C)
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Q: If the knowledge that an event A has occurred implies that a second event B cannot occur, then the…
A: a) Event A has occurred and event B can not occur then the events A and B are said to be disjoint .…
Q: Given that P(A) = 0.01, P(B) = 0.11, and P(A and B) = 0.0010, are events A and B independent? %3D…
A: Answer
Q: Suppose that A and B are events such that P (A|B) = P (B|A) , P(AUB) = 1, and P(An B) > 0. Prove…
A: Solution: From the given information,
Q: Given that P(A) = 0.06, P(B) = 0.23, and P(A and B) = 0.0258, are events A and B independent? Yes,…
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Q: An experiment can result in one of five equally likely simple events, E1, E2, ..., E5. Events A, B,…
A: It is given that P(A)=0.4, P(B)=0.8, and P(C)=0.4.
Q: If two events are mutually exclusive, then they are independent. select one : a. True b. False
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Q: 7. If two events A and B are mutually exclusive, then P(A N B) = computed from the fomula P(A U B) =…
A: If two events A and B are mutually exclusive, then PA∩B=______. As a result, PA∪B can be computed…
Q: If the probability of one event has no influence on the probability of the other then the events are…
A: If the probability of one event has no influence on the probability of other then the event are said…
Q: Consider two events A and B. Use Venn diagram to show that (AU B) \ A = B\ A
A: For any two events A and B. Using venn diagram, we need to show that: (AUB)\B = B\A
Q: Consider two events B and C, such that P(B) = 0.28, P(C) = 0.46, and P(C n B) = 0.2, then P(C n B)…
A: Given that P(B) = 0.28, P(C) = 0.46, P(C' AND B) = 0.2
Q: If two events are independent with P(A) = 0.6 and P (B ) = 0.35 Is A and B are complementary events…
A: Given: P(A)=0.6 P(B)=0.35
Q: If two events, Event A with probability P(A) and Event B with probability P(B) are independent, then…
A: Given that two events, Event A with probability P(A) and Event B with probability P(B) are…
Q: Theorem 3.10. If the events A and B are such that P(A) #0, P(B) ±0 and A is independent of B, then B…
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Q: CONSIDER two events A and B PROVE that if Bc A then P(B) < P(A)
A: We have to answer question based on set
Q: 2. If A and B are mutually exclusive events and P(A) = 0.3 and P(B) = 0.5, find a.) P(A U B) b.) P…
A: Given A and B are mutually exclusive events and P(A)=0.3 and P(B)=0.5, Find a).P(AUB)b).P(A)'…
Q: Answer true or false to the following statement and justify your answer: If event A and event B are…
A: The statement is “If events A and B are not mutually exclusive, neither are events A, B, and C for…
Q: If A and B are independent events associated with an experiment P(A) = 0.3, P(AUB) = 0.72, then the…
A:
Q: : If A, B, C are mutually independent events then A UB and C are also independent.
A: Answer: For the given data,
Q: Prove that if two events, A and B, are mutually exclusive, then P(A | A U B ) = P(A) / ( P(A) + P(B)…
A: If two events are mutually exclusive, then the two events are disjoint event.In other words, if A…
Q: Let A and B be two events with P(A) = 0.13, P(B) = 0.04 and P(AUB) = 0.1323. %3D %3D Then, A and B…
A: If Two events are Disjoint their intersection will be zero. If two events is independent their…
Q: Let A, B, be two independent events such that P(A) = P(B) = 0.3 then P(A UBC) =
A: Given that PA=PB=0.3 A and B are independent events. Hence, P(A and B)=P(A)*P(B)=0.3*0.3=0.09
Q: If two events A and B are not mutually exclusive, then P(A U B) can be computed by the formula P(A U…
A: Given that A and B are not mutually exclusive. So it will roughly look like:
Q: If A & B are two events and p(B) ≠ 1, prove that p(A/B') = [p(A) - p(A∩B)/[1 - p(B) where B'…
A: We have, two events A and B thus, P(A|B')=P(A∩B')P(B') ......(1)We know that,…
Q: If P (Event A)=0.2 and P(Event B)=0.3, and the two events are disjoint, then P (Event A and Event B)…
A: Disjoint events : if two events A and B are disjointevents then the two events can not occure at the…
Q: Let A and B be two events such that P(AC) = 0.70, P(B) = 0.50, and P(A U B) = 0.60. What is P(An B)?
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Q: If A, B, C, and D are independent events. Prove that A U B and C – D are independent.
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Q: IJ A and B are independent events, prove that the events A and B, A and B; and A and B are also…
A: Answer: For the given data,
Q: Show that for two events A and B, any P(A N B) s P(A) s P(A U B) s P(A) + P(B)
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Q: An experiment can result in one of five equally likely simple events, E1, E2, . . . , E5. Events A,…
A:
Q: Consider the problem of selecting two applicants for a job out of a group of five and imagine that…
A: Probability: A probability helps us in finding assumed chances of an outcome in a range between 0…
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