Suppose that A and B are events such that P(A) = 1/3, P(B) = 1/5, and P(A|B) + P(B|A) = 2/3. What is P(A ∩ B) (a) 1/12 (b) 2/12 (c) 3/12 (d) 4/12 (e) None of the above

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: Assume that events A and B are independent, and C ⊂ A, and C ⊂ B. Moreover, P(A) = 1/2, P(B) = 2/3,…

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Q: Suppose E and F are events such that n(E) = 14, n(F) = 15, and n(ENF) = 2. a) Find P(E|F). b) Find…

A: Givenn(E)=14n(F)=15n(E∩F)=2Total no. of events(n)=14+15-2=27

Q: 3. A and B are events such that P(A) = 0.2 and P(A U B) = 0.5. Find P(B) in each of the following…

A: There are two events A and B are given.The given probabilities are as follows

Q: Suppose that the events A, B, and C are independents, where P(A)= 1/2, P(B)=1/3, and P(C)= 1/4. What…

A: Given that A, B, and C are independents. So,…

Q: True or False: for each of the following statements, decide if it is true or false. If it is true,…

A: As per given by the question, there are two statement are given and find whether the statement true…

Q: This problem hopes to show you the difference between independent events, where you use P(A and B) =…

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Q: Suppose that AA and BB are two events for which P(A)=0.32P(A)=0.32, P(B)=0.73P(B)=0.73, and…

A: Given that : P(A)=0.32 P(B)=0.73     and    P(B|A)=0.37 By using the properties of basic and…

Q: Let A and B be independent events with P(A) = P(An B) = P(AUB) = 1 ·|6 1 and P(B) = Find P(An B) and…

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Q: B) are disjoint, what is the probability of their union? a.) P(A) + P(B) b.) P(A)P(B) c.) 0 d.)…

A: As given that events A and event B are disjoint. It is asked to find the probability of their union.

Q: 6 involving independent and disjoint events. For this problem, assume that Pr[A∪B]=0.55 and…

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Q: Let A and B be events such that P(A)=1/4, P(A or B)=1/3, and P(A and B)=1/5. DetermineP(B)

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Q: P(B1)=4,P(B2)=6 and that the bids are independent

A: Given that, Let B1 be the event that the first bid is successful and B2 did the second bid…

Q: Which of the following is NOT necessarily true for mutually exclusive events A and a) P(A NB)=0 c)…

A: Mutually Exclusive events: If A and B mutually exclusive events, then PA∩B=0. a) From the mutually…

Q: Suppose that A and B are events such that P(A) = 1/3, P(B) = 1/2 and P(A ∪ B) = 5/6. Find (a) P(A ∩…

A:

Q: The general multiplication rule says that P(A and B)=_______If A and B are events, the…

A: Here given , The general multiplication ,  multiplication rule  P(A and B) = P(A). P(B).

Q: Given  P(A) = 0.3, P(b) = 0.5 and P( A and B ) = 0.2.       Are the events A,B independent ?…

A: Thank you for posting the question. Since you have asked multiple question(Different questions), we…

Q: "Events AA and BB are mutually exclusive if they can not occur simultaneously." This statement is…

A: Given information- We have given that A and B are mutually exclusive. A and B are mutually exclusive…

Q: If A and B are independent events, then ... None of the above OP(AUB)=P(A)×P(B) OP(A U B) = 1OP(An…

A: If events A and B are independent, it means that the occurrence or non-occurrence of one event does…

Q: Consider two events A and B such that P(A) = 1/2 and P(B) = 1/3. Find P (A n BC) under each of the…

A: P(A)=1/2, P(B)=1/3