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

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: 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: 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…

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Q: Let A and B be two events such that p(A) = 0.4 and P(BA) = 0.2. Then P(BnA) = 0.4 0.7 0.6 0.5

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Q: 1. Let A and B be independent events such that P(A), P(B) > 0. Is it possible that A and B are…

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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: Let A and B be events with P(A) = 0.7, P(B) = 0.9, and P (A and B) = 0.6. Compute P (A or B) Are A…

A: a.

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: Given P(An B') = 0.25, P(A) = 0.48 and P(B) = 0.42. Find P(A n B). Is A and B mutually exclusive…

A: (1) Let A and B are two events The known probabilities are,

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 B be events such that P (A) = 4/10 and that P (A∪B) = 7/10 Find the probability of B…

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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: 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: 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: (a) Two independent events, A and B, are such that, P(A) = 0.7 and P(B) = 0.4, calculate: (i) P(An…

A: We have to solve given problem:

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 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: 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: If A, B, and C are three events, prove that P(ANBOC) >1– P(A)– P(B)– P(C)

A: There are three events A,B and C. So, From De Morgan's law, P(A ∪ B ∪C) = P(A∩B∩C)⇒P(A ∪ B ∪C) = 1 -…

Q: Let A, B, and C be independent events such that P[A] = 0.5, P[B] = 0.6, and P[C] = 0.1. Calculate…

A: P(A ∪ B ∪ C) = P(A) + P(B) + P(C) − P(A ∩ B) − P(A ∩ C) − P(B ∩ C) + P(A ∩ B ∩ C) P(A) = 0.5 P(A')…

Q: If A and B are events such that ​P(A)=0.2 and ​P(A∪​B)=0.4​, find​ P(B) when ​(a) A and B are…

A:

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: 3. Let C and D be events with P(C) = 0.1, P(D) = 0.6, and P(C U D) Are C and D independent? Explain.

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Q: Let A and B be 2 events such that P(A)= 0.3 and P(B) = 0.4 and P(A U B) = 0.6. Then the value of P(B…

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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: 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: Let A and B be events of positive probability. Prove that P(A|B) > P(A) if and only if P(B|A) > P(B)

A: Let , A and B be the two events. We have , P(A)&gt;0 and P(B)&gt;0 i.e. both have positive…

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: 5. Let A and B be events such that 0 < P(A) < 1 and 0 < P(B) < 1 a. Show that if A and B are…

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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: If A and B are mutually exclusive events, then prove that P ( A )<P ( B° )

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Q: Let A and B be two events such that P (A ∪ B) = 0.6 and P (A ∪ Bc ) = 0.8 Find P (A).

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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: Show  that :If A and B are independent, it follows that the following events are also independent:…

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Q: If A and B are two independent events where P(A) = 0.2 and P(B) = 0.3 , then P(AN B) = %3D O 0.2 0.5…

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Q: Let A and B be events such that 0

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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: 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: 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: 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 ∪…