In parts Ce) and Cb), idenfy whether the events are Musul Exclusive, Independent, or Neither (events cannot be both sive, Independent, or Neither (events cannot be both disjoint and independent). a) You and a randomly selected student from your class both earn A's in this course Mutually Exclusive O Neither Independent b) You and your class partner both eam A's in this course. Mutually Exclusive Neither Independent c) If two events can occur at the same time, they must be independent False True

Q: If A and B are events such that ​P(A)=0.6 and ​P(A∪​B)=0.8​, find​ P(B) when ​(a) A and B are…

A: (a)   Obtain the probability value of P(B) if A and B are mutually exclusive events. The probability…

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: 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: A card is drawn from a deck of cards. Events E1, E2, are defined as follows: E1: Getting a face card…

A: Given that E1: Getting a face card E2: Getting an ace card Are E1 and E2 mutually exclusive ?

Q: Given P(A) = 0.37 , P(B) = 0.38 , and P(AorB) = 0.27 , are events A and B mutually exclusive?

A:

Q: In parts (a) and (b), identify whether the events are Mutually Exclusive, Independent, or Neither…

A: Independent events: Two events A and B are said to be independent, if probability of occurrence of…

Q: Prove that if P( A ) = 7/50 , P ( B ) = 1/4 and P(A U B) =3/10, then A and B are inclusive events

A:

Q: The intersection of event A and B is often denoted as "A or B" O True O False to

A: Please find the handwritten solution.

Q: If X and Y are mutually exclusive events, then if X occurs _______.     Y must also occur…

A: X and Y are mutually exclusive events. Mutually Exclusive Events: If X and Y are mutually exclusive…

Q: Suppose that A and B are non-mutually exclusive events such that 17 . P(A) = 21,P(B) = 2121 and P(A…

A: It is given that  P(A) = 8/21 P(B) = 12/21 P(A or B) = 17/21

Q: In how many different order could the police department arrange six suspects in a police lineup if…

A: In this question we will use basic of permutations and combinations and concept of probability and…

Q: Suppose that A, B are two events such that P(A) > 0 and P(B) > 0.  If A and B are not disjoint, then…

A:

Q: Prove or disprove that for any two events A, and A2, P[A, n A-] 21- PÍAG] – P[A£]

A:

Q: If A denotes some event, what does A denote? If P(A) = 0.996, what is the value of P(Ā)? ..... What…

A:

Q: Are the events of rooting for the away team and wearing blue independent? Are they mutually…

A: Let A be the event that a fan is rooting for the away team.Let B be the event that a fan is wearing…

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: P(A) = 0.3, P(B) = 0.4, and P(A or B) = 0.7, then   a. A and B are mutually exclusive (disjoint)…

A: It is given that  P(A) = 0.3 P(B) = 0.4 P(A or B) = 0.7

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: The word OR creates A new event out of two events A and B. The new event consist of A. only those…

A:

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: Construct a Venn diagram that portrays four events,A,B,C, and D that have the following properties:…

A: The Venn diagram is constructed using the following properties:Events A, B, and C are mutually…

Q: If the outcome of event A is not affected by event B, then events A and B are said to be…

A: Definition of independent events.

Q: If P(A) = 0.4, P(B) = 0.2, and P(AU B) = 0.6, then P(AN B) = (a) Are events A and B independent?…

A:

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:

Q: Construct a Venn diagram representing the event a.(A&amp;(not B)).b.((A or B)&amp;(not (A&amp;B)))

A: a)Venn diagramVenn diagram is a diagrammatic representation of sets which shows the relationship…

Q: Two events, M and N, are such that P(M) = 0.6, P(M ∩N) = 0.2, P(M ∪N) = 0.85 Find (i) P(N |M) [2]…

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:

Q: f A and B are events with P(A)=0.6, P(AorB)=0.98, P(AandB)=0.02, findP(B)

A: It is given that P(A)=0.6, P(A or B)=0.98 and P(A and B) =0.02.

Q: In a basketball arena, • 70% of the fans are rooting for the home team. • 25% of the fans are…

A:

Q: Let C and D be events satisfying Pr(C∪D)=Pr(C)+Pr(D). Which of the following statements is/are true?…

A: (a) We know that  P[A∪B]=P[A]+P[B]-P[A∩B], so by this we get from the question information that…

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: Which of the following statements is false? O Two complementary events cannot occur at the same…

A: complementary events are those events  where only two possible outcomes are there.   Independent…

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

A:

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: Given P(A) = 0.34, P(B) = 0.60 , and P(AorB) = 0.24 , are events A and B mutually exclusive?

A: Let A and B are two events The given probabilities are, P(A) = 0.34, P(B) = 0.60 ,  P(A or B) = 0.24…

Q: If P(A) = 0.2, P(B) = 0.3, and P(AU B) = 0.5, then P(AN B) = (a) Are events A and B independent?…

A: The probability rule of addition gives us PA∪B = PA+PB-PA∩B

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: 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 denotes some event, what does Ā denote? If P(A) = 0.996, what is the value of P(Ā)? ..... What…

A:

Q: If A, B, C, and D are independent event Prove that AUB and C- D are independent.

A:

Q: Are these events mutually exclusive (E) or mutually inclusive (I)?    Blank 4 4. Randomly drawing…

A:

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: Consider five mutually exclusive events, V, W, X, Y, and Z, respectively, where P(V) = 0.08, P(W) =…

A: Mutually Exclusive Events :  A and B are mutually exclusive events if they cannot occur at the same…

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: 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: Let A and B be events so that p(B|A) = .8, p(BJĀ) = 4, and p(B) = .62. What is p(A)?

A:

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: If A, B, C, and D are independent events. Prove that A U B and C – D are independent.

A:

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