Find answers to questions asked by students like you.
Q: 1) Prove that if A and B are events, then Pr[A] – Pr[B] < Pr[A\ B]
A: Hi! Thank you for posting the question. Since you have posted multiple questions, we are answering…
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: 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: If A, B, C, and D are independent event Prove that AUB and C- D are independent.
A: Click to see the answer
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: Prove that a pair of events A and B cannot be simultaneously mutually exclusive and independent.
A: Hello. Since your question has multiple parts, we will solve first question "Prove that a pair of…
Q: Prove that a pair of events A and B cannot be simultaneously mutually exclusive and independent.
A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…
Q: Prove that if A and B are events, then Pr[An B] > Pr[A] + Pr[B] – 1.
A: Click to see the answer
Q: Choose the following statements that are true for any events A, B. Pr{AU B} = Pr{A} + Pr{B} –…
A: Answer - Choose the following statements that are true for any events A, B.
Q: If A, B, C, and D are independent events. Prove that A U B and C – D are independent.
A: Click to see the answer
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: 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: Two events, M and N, are such that P(M) = 0.6, P(M ∩N) = 0.2, P(M ∪N) = 0.85 State, with reason,…
A: Solution
Q: One satellite is scheduled to be launched from Cape Canaveral in Florida, and another launching is…
A: let event A: the vandenberg launch goes off on schedule. and event B: the cape canaveral launch goes…
Q: 2. Let 0 0, P(B| A) = P(B|A), then that event A and B are independent. prove
A: We need to prove, P(AnB) = P(A)P(B)
Q: In a basketball arena, • 70% of the fans are rooting for the home team. • 25% of the fans are…
A: Click to see the answer
Q: In a basketball arena, 70% of the fans are rooting for the home team. 25% of the fans are wearing…
A: From the given data: P(A)=0.3 P(B)=0.25 P(A and B)=0.2
Q: In a basketball arena, • 70% of the fans are rooting for the home team. • 25% of the fans are…
A: Here, A is the event of getting a fan is rooting for the away team and B is the event of getting a…
Q: If events A, B, and C are independent, show that(a) A and B ∩ C are independent;(b) A and B ∪ C are…
A: Click to see the answer
Q: Show that if events A and B obey the multiplication rule, P(A and B) = P(A) P(B), then A and the…
A: It is given that A and B follows the rule P(A∩B)=P(A)·P(B) that means the events A and B are…
Q: If A and B are independent events, prove that the following pairs of events are independent: Ac and…
A: Click to see the answer
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: A bag contains 5 green marbles, 8 blue marbles, and 6 red marbles. Let's call the event A "Drawing a…
A: Two events are said to be mutually exclusive if they cannot occur at the same time. If two events A…
Q: Answer true or false to the following statement and justify your answer: If event A and event B are…
A: Click to see the answer
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 event A and B are not mutually exclusive, neither are events A, B, and C for…
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: Suppose a card is drawn from a standard 52 cards deck. Let A denote he event "the card drawn is…
A: Click to see the answer
Q: If event A is a subset of event B, then P(AN B )is
A: Ans: If event A is a subset of event B, then P( A∩Bc ) is
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: In parts (a) and (b), identify whether the events are Mutually Exclusive, Independent, or Neitther…
A: a) Ans: Independent Reason: since the score achieved by one is independent of the other
Q: In parts (a) and (b), identify whether the events are Mutually Exclusive, Independent, or Neithe…
A: (a) If the probability of occurrence of one event is not affected by the probability of occurrence…
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: If A denotes some event, what does A denote? If P(A) = 0.996, what is the value of P(Ā)? ..... What…
A: Click to see the answer
Q: Let A ,B and C be three disjoint events defined over the same place S. Assume AUBUC = S, P(A) = 0.1,…
A: A, B and C be three disjoint events hence, P(A^B)=0 P(A^C)=0 P(B^C)=0 P(A^B^C)=0 P(A)= 0.1 P(B)=0.2…
Q: Let A, and A, be mutually exclusive and exhaustive events, with P(A,)=.10 and P(A,)=.25. Let B by…
A: Solution: 15. From the given information,
Q: If A denotes some event, what does Ā denote? If P(A) = 0.996, what is the value of P(Ā)? ..... What…
A: Click to see the answer
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: Given P(A) = 0.15, P(B) = 0.45 , and P(AorB) = 0.35 , are events A and B mutually exclusive?
A: Given, PA=.45, PB=.15 PA or B=.35 If two events A and B are mutually exclusive, then PA or…
Q: Given P(A) = 0.37 , P(B) = 0.38 , and P(AorB) = 0.27 , are events A and B mutually exclusive?
A: Click to see the answer
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)
A: Click to see the answer
Q: Florin Frenti operates a small, used car lot that has three Mercedes (M1, M2, M3) and two Toyotas…
A: Florin Franti operates a small, used car lot that has three Mercedes (M1, M2, M3) and two Toyotas…
Q: A bowl contains 5 white balls, 10 red balls, and 15 blue balls. You are to randomly select two balls…
A: Given problem Given that A bowl contains 5 white balls, 10 red balls and 15 blue balls . You are…
Q: Given that A and B are two independent events. Give your own example to show the independent event…
A: Click to see the answer
Q: Given that A and B are two independent events. Give your own example to show the independent event…
A: Independent events are A and B.
Q: If A and B are independent event then O a. P(A and B) = P(A) - P(B) %3D O b. P( A and B) = P(A) %3D…
A: Given : A and B are independent event then Correct option is C
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.
A: Click to see the answer
Q: Given P(A) = 0.20, P(B) = 0.30, and P(A or B) = 0.50, are events A and B mutually exclusive?
A: Solution: Mutually exclusive events: Two events A and B are said to be mutually exclusive when the…
Q: Let A and B be events with =P(A)= 0.2, P(B)=, 0.88, and P(B|A)=0.6.…
A: Click to see the answer
Q: A1, A2, and A3 are mutually exclusive and exhaustive events such that P(A1) = 0.2, P(A2) = 0.5, and…
A: Let are mutually exclusive and exhaustive events. Let B be the event The known probabilities are,
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…