Let A and B be events. Point (prove) that:   a. P(A \ B) = P(A) − P(A ∩ B).    b) If 0 < P(B) < , and P(A|B) = P(A|Bc), then A⊥B.

Q: Let A and B be two events such that P(A|B)=P(A|BC), where BC is the complement of B), and 0 < P(B) <…

A: We use the conditional probability formula to prove that A and B are independent.…

Q: Let A, B be two mutually exclusive events such that AUB = 2, p(A) = 4p(B). Find p(B - A) Select one:…

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Q: a student takes a true false test that has 6 questions and guests randomly at each answer. Let x be…

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Q: 4. Show that an event A is independent of itself iff P(A) is either 0 or 1.

A: Proof: PA=PA∩A=PAPA  Since A is independent itself.⇒PA1-PA=0PA=1  Since P(A)&gt;0

Q: We will define the conditional probability of A given X as any random vari- able P(AIX) over (N, F,…

A: To prove that two versions of  differ in a set of probability zero, we'll use a proof by…

Q: Each of 12 laptops was returned to the dealer due to a strange sound from the fan when they were…

A: The number of laptops are 12. The number of faulty laptops are 7. The number of laptops have less…

Q: Be sure to keep up to 4 decimal places for all answers Suppose that P(A)=1/4 and P(B)=1/3. Assuming…

A: P(A) = 14P(B) = 13mutually exclusive events.

Q: Show that for any events E and F, P(E|E U F) 2 P(E|F). Hint: Compute P(E|E n F) by conditioning on…

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Q: events x and y are such that px = 0.35 and px ∪ y = 0.80. given that x and y are independent and…

A: Given That, p(x)=0.35 p(x ∪ y )=0.80 Given that x and y are independent and non-mutually exclusive…

Q: Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L), or go…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Theorem 3.16. For any three events A, B and C, Р (AnB IC)+ P (AnBIC)- Р (AI C)

A:

Q: Claim: A majorityof adults would erase all of their personal information online if they could. A…

A: The claim is that majority of adults would erase all of their personal information online if they…

Q: For any two events A and B and P(B)÷ 1 and A N B = Ø, find weather the following statement is true…

A: GivenTw events A and B P(B) ≠1A∩B = ϕ So A and B are mutually exclusive events, So P(A∩B)=0. The…

Q: Q15: Let A and B be two events such that Let A and B be two events such that P (A) > 0 and P (B) >…

A: When two events are independent PA∩B=PA×PB And PA∩B=0 can only be possible when either PA=0 or PB=0

Q: At the Skittles factory, a bag of Skittles is filled by a mechanical scoop. The scoop picks up 9,…

A: The objective of this question is to find the variance of the number of Skittles scooped up by the…

Q: Show that for any 1 ≤k≤n. T (1) = n²(n²-1²)...(n² (k − 1)²) 1.3.5 (2k-1)

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Q: Show: P(EG) ≤ P(F|G₂) = P(E) ≤ P(F), given that E, F, G₁, G2,.., G

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Q: ​Claim: A minority of adults would erase all of their personal information online if they could. A…

A: Here we want to express claim in symbolic form.

Q: For any three events A, B and C P ( A U BUC) = P(A) + P (B ) + P ( C ) – P ( A OB)-P( BnC) -P(CnA)+…

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Q: Let A, B, and C be three events, such that each event has a probability of 1/2, each intersection of…

A: GIVEN          Let A, B, and C be three events          P(A)=P(B)=P(C)=1/2…

Q: ​Claim: A minority of adults would erase all of their personal information online if they could. A…

A: From the provided information, Sample size (n) = 688 Sample proportion (p̂) = 0.37

Q: Find P(P(P(empty set))) , where P(A) denotes the power set of A.

A: Given  A = Empty set  To find : P(P(P(empty set)))

Q: Example: Let x=1,2,3,4,5 15 P(x) = show that p(x) is p.d.f elsewhere

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Q: Assume two set S, T of real numbers are both bounded (i.e., are both bounded above and bounded…

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Q: If S and T are mutually exclusive events then P(S|T) is P(SnT) P(S) P(SnT) o P(T) 1 近

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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: Show that if A and B are sets, then P(A) u P(B) C P(A u B), where P(A) denotes the power set of A

A: For a set A, the set of all its subsets is called the power set of A. Now, consider two sets A and…

Q: Vx(Fx – Gx) .: VxFx V V×GX

A: Let domain is set of all real numbers.

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

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Q: (a) Let A = {(−1)kk² : k≤N}, B = {nЄN:n < 100}, C = (–49,16], D= [−25,100). Write down the following…

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Q: SOLVE STEP BY STEP IN DIGITAL FORMAT XXXXXXXXXXXX Show that if A1, XXXX An are independent events…

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Q: Prove that P(A | B) = P(B | A)P(A)/P(B) whenever P(A)P(B) 0. Show that, if P(A | B) > P(A), then P(B…

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Q: Events X and Y are such that PP(XX) = 0.30 and PP(XX ∪ YY) = 0.70. Given that X and Y are…

A: As X and Y are independent and mutually exclusive,  P(X∩Y)≠0 , therefore, P(X∩Y)=P(X).P(Y) .