IJ A and B are independent events, prove that the events A and B, A and B; and A and B are also independent.

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: Let A and C be two independent events such that P(A) 0.2 and P(C) 0.3 P(ĀNC) = 0.24 None of other…

A: Given that A and C be two independent events such that P(A) = 0.2 and P(C) = 0.3 .  Than we have to…

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: let A ,B be two disjoint events such that P(B) = 0.1 then P(A° \ B ) = 1 0.5 Other

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Q: a) Let A and B be independent events. Denote by the events AC and BC the complements of the events A…

A: Since A and B are Independent events,                                                        P(A∩B)…

Q: 3. A and B are two events such that P(A) =, P(A|B)= and P(A|B')=;. %3D Show that P(AOB) : 64

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Q: 1. Let A and B be events such that, P(A) = 0.6, P(B) = 0.7, P(A N B) = 0.4 Find %3D a. P(A U B) b.…

A: Given that, A and B are events, PA=0.6PB=0.7PA∩B=0.4

Q: 5. Let A,. A. A, be three independent events. Prove or disprove that Af. Aş, and A are independent.

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Q: let A and B be two events in an outcome space M such that M = A U B, P (A) = 0.65 and P (B) = 0.75.…

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Q: how that if A1, A2, and A3 are independent events, then P(A1|A2 and A3)

A: Given that A1, A2, and A3 are independent events.

Q: If P(A)=0.2, P(B)=0.1, and P(A∪B)=0.3, then P(A∩B)= Are events A and B independent? Are A and B…

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Q: 2. Let A and B be events. Then P(AAB) = P(A \ B) + P(B \ A). %3D TRUE O FALSE

A: we only solve one problem at a time so please post them one by one.

Q: Given that A and B are independent events, show that ?̅ and B are also independent events

A: Given: Given that A and B are independent events, show that ?̅ and B are also independentevents

Q: iven that P(A) = 2/3 , P(B) = 1⁄2 , P(A ∩ B) = 1/3 and P(A ∪  B) = 5/6, state whether each of the…

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Q: Let A, and A, be two events such that P[A] = 1/2. P[A2] = 3/5 and P[A2|A1] = 2/5 Then: %3D O PLA, n…

A: Solution: From the given information,

Q: Show that if A and B, (n = 1,2,3, . -) are events, then An (U Bn) = U (AN Bm)

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Q: Let A and B be independent events with P(A) " and P(B) =. Find P(AN B) and P(A U B).

A: Given that P(A) = 1/8 P(B) = 1/5

Q: 10. Let A and B be events such that Pr[B] = 0.7,Pr[A U B] = 0.9, Pr[A|B] = 0.3. Find Pr [A]. %3D %3D

A: Provided information: P(B)=0.7P(A∪B)=0.9P(A|B)=0.3

Q: 1. Let A and B be two events such that P(A) = 0.4, P(B) = 0.7, P(A U B) = 0.9 %3D a) Find P(A n B).

A: Given: P (A) = 0.4 P (B) = 0.7 P (A U B) = 0.9   a) P (A ∩ B) = ?

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: Let A and B be events where P(A) = 1/3 and P(B) = 1/4. Show bounds for P(A intersection B)

A: P(A) = 1/3, P(B) = 1/4.

Q: Let A and B be two events such that P(A/B) = P(B/A) = and P(An B) = 1/ 1 Then P(AUB) = 2/3 3/4 1/3 O…

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Q: If A and B are independent events, prove that the following pairs of events are independent: Ac and…

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Q: If P(A) = 0.2, P(B) = 0.3, and P(A U B) = 0.48, then P(An B) =|. (a) Are events A and B independent?…

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Q: uestion 16 For any two events A and B to be not independent, P(AN B) = P(A).P(B) True False

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Q: Let A and B be events where P(A) = 1/3 and P(B) = 1/4. Show bounds for P (A U B) and P (A…

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Q: extbook 2.23: If A and B are events and B C A, why is it “obvious" that P(B) < P(A)? [hint: Use the…

A: *answer:

Q: If A and Bare two independent events where P(A) = 0.2 and P(B) = 0.4, then P(ANB) = %3D • 0.2 • 0.4…

A: Solution-: We have,  and A and B are independent event We find,

Q: Let A and B be two events such that P(A)=1/7, P(AUB)=1/2, and P(AB)=1/12. Determine P(B)

A: From the provided information, P (A) =1/7 P (A Ս B) = 1/2 And P (AB) = 1/12

Q: Prove: If A and B are events, then P(B) > P(A ∩ B)

A: Solution-: Given: A and B are events. We want to prove P(B)≥P(A∩B)

Q: Prove that if A and B are events, then Pr[An B] > Pr[A] + Pr[B] – 1.

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Q: Let A and B be mutually exclusively  events with P(A)=0.24 and P(B)=0.34

A: If A and B are mutually exclusive events then, P(A ∩ B) = 0 Now we know that P(A U B) = P(A) + P(B)…

Q: Let A and B be two events such that P(A)=0.5, and the probability that neither occurs is 0.3. Find…

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Q: Let A and B be any two events defined on S. suppose that p(A)=0.2, p(B)=0.7, and p(A and B)=0.3, the…

A: It is given that, p(A) =0.2 p(B) =0.7 and p(A and B) =0.3

Q: Let A and B be events with P(A) = 0.5, P(B) = 0.4. Assume that A and B are independent. Find P(A and…

A: Here the events are indepenedent P(A) = 0.5 P(B) = 0.4

Q: If A and B are disjoint events such that P(A) =0.30 and P(B)=0.50 then P(BNAC) %3D

A: It is given that, A and B are disjoint events i.e. P(A ∩ B) =0 We have P(A) =0.30 and P(B)=0.50

Q: Given P(A)=0.5 and P(B) =0.3 a) if A and B are mutually exclusive events, compute P(A or B)

A: Two events are said to be mutually exclusive events, if two events can not occur simultaneously.…

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: 2. A and B are events such that P(A) = 0.3, P(B) = 0.4, P(A/B) = 0.5. Calculate: (1) P(AB) and P(A +…

A: Answer :- Given A and B are two events.  where P(A) = 0.3,  P(B) = 0.4,    P(A|B) = 0.5…

Q: Prove the following theorem: If A and B are independent, then so are the following pairs of events:…

A: Given, A and B are independent event i.e. Now, Therefore, A and Bc are independent

Q: 1. Let A and B be random events. Show that if AC B then P(A)<P(B).

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Q: Suppose two doctors, A and B, test all patients coming into a clinic for syphilis. Let events A+ =…

A: Given: The provided events are: A+={ doctor A makes a positive diagnosis}.  B+= {doctor B makes a…

Q: Exercise 24 Let A and B be 2 events : P(A) and P(B') 3 Can A and B be mutually exclusive? Why?

A: It is given that, P(A) =1/3 and P(B') = 1/4. This implies that P(B) =1-1/4 =3/4 We know that the…

Q: If A and B are two independent events where P(A) = 0.2 and P(B) =0.4, then P(ANB) = %3D O 0.4 O 0.2…

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Q: Let A and B be events with P(A) = 0.1 and P(B) = 0.4. Assume that A and B are independent. Find P(A…

A: We have given that,  A and B are two independent events with     P(A) = 0.1 and P(B) = 0.4 Then, We…

Q: 1. Let A and B be independent events with P (A) = 0.7 and P (B) = 0.2. Compute: (a) P (A∩B) (b) P…

A: Given: PA=0.7PB=0.2 A and B are independent events. 1. (a) P (A∩B) is obtained as below:…

Q: Prove that if A and B are events, then Pr[A] – Pr[B] < Pr[A\ B]

A: LHS =PA-PB=PA-PA∩B In LHS, we are subtracting, therefore, the value of LHS will be small

Q: 1. If P(A|B) = 0.5 and P(B) = 0.5, then the events A and B are independent. * %3D true false

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Q: Prove that if E1, E2,.., En are independent events, then P(E, U E2 U .. U En) = 1- | 1– P(E;)] i=1

A: Given that, E1, E2, ........., En are independent events. We need to prove that: P(E1∪E2 ∪…