5. If the events A and B happen to be mutually exclusive then, a. P(AU B) = P(A) + P(B) b. P(AN B) = P(A) + P(B) c. P(AN B) = P(A) P(B) d. P(A UB) = P(A) · P(B)

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: Given that P(A) = 0.17, P(B) = 0.08, and P(A and B) = 0.0136, are events A and B independent?

A: To find that both are independent

Q: a. Assume that the selections are made with replacement. Are the events independent?

A: here use given contingency table

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: nsider event A and event B, if ?(??)=0.46 and ?(?)=0.58, If ?( ?∪ ?)=0.8. a. Find ?(?∩?). b. Could…

A: It is given that the There are two events A and B such that  P(A) = 0.46, P(B) = 0.58, P(A∪ B) = 0.8…

Q: if A and B are disjoint events with P(A) = 0.20 and P(B) = 0.50 Then P(A/AUB) =

A:

Q: If A,B,C are mutually exclusive events with PĀ) = 0.45, P(B) = 0.36, then P(AN B) = a. 0.91 O b.…

A: PA=0.45 PB=0.36

Q: If A and B are events such that ​P(A)equals=0.60 and P(A∪​B)equals=0.70​, find​ P(B) when ​(a) A…

A: (a)If events A and B are mutually exclusive events, then, P (A or B) = P(A)+ P(B).Or, P(B) = P (A or…

Q: Use Venn diagrams to verify that(a) (A ∪ B)∪ C is the same event as A ∪(B ∪ C);(b) A ∩(B ∪ C) is the…

A: Consider event (i.) as (A ∪ B)∪ C and event (ii.) as A ∪(B ∪ C)

Q: For the given pair of events A and​ B, complete parts​ (a) and​ (b) below.   ​A: When a page is…

A: Consider the events as:A: When a page is randomly selected and ripped from a 21 pages’ document and…

Q: Each of a sample of four home mortgages is classified asfixed rate (F) or variable rate (V).a. What…

A: As per bartleby guidelines for multiple subparts only first three subparts are to answered please…

Q: For two events E and F, P(E) = 0.30, P(F) = 0.40, and P(E U F) = 0.70. Are E and F mutually…

A: Introduction: The occurrences that cannot occur or cannot occur at the same time are said to be…

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, B, C are are independent of C. independent events, show directly that both AUB and A\ B

A: Given that A, B, and C are independent means that, A∩B=B∩C=C∩A=A∩B∩C=φ.... (1) Now, A∪B be can be…

Q: 14. If the outcome of event A is not affected by event B, then events A and B are said to be : A.…

A:

Q: Suppose that A,B, and C are independent events such that P(A) = 0.8,P(B) = 0.5, and P(C) = 0.3. Find…

A: The Special Multiplication Rule

Q: Let's define two events A and B where P(A)=0.8 and P(B)=0.4. If P(A ∪ B)=1, what is P(Ac ∪ Bc)? 0.7…

A:

Q: Suppose that A,B, and C are three events that cannot all occur simultaneously. Does this condition…

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

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: Answer true or false to the following statement and justify your answer: If event A and event B are…

A:

Q: If A and B are any two events with P(A) = 0.9 and P(B|A) = 0.5, then the probability of A and B is?

A:

Q: Let A, B, and C be independent events with P(A)= 0.8, P(B)= 0.3, and P(C)=0.4 Find P(A and B and C).…

A: given A, B, and C be independent events  P(A)= 0.8, P(B)= 0.3, and P(C)=0.4 P(A and B and C ) = ?

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: Consider two events A and B. Use Venn diagram to show that (AU B) \ A = B\ A

A: For any two events A and B. Using venn diagram,  we need to show that: (AUB)\B = B\A

Q: If event A and event B are as above and event A has probability 0.3 and event B has probability 0.1,…

A: The following information has been given: Event A has probability P(A)=0.3 Event B has probability…

Q: Suppose that a family is leaving on a summer vacation in their camper and that M is the event that…

A:

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: we have 100 students in the Institute of Computing, Kohat University of Science and Technology. Out…

A: Probability is defined as the sum of favorable ways of an events divided by the total number of…

Q: Theorem 3-9. If A, B, C are mutually independent events then A UB and C are also ndependent.

A:

Q: If A and B are two independent events with P(A) = 0.15 and P(B) = 0.4, then P(AUB) is

A:

Q: If two events, Event A with probability P(A) and Event B with probability P(B) are independent, then…

A: Given that two events, Event A with probability P(A) and Event B with probability P(B) are…

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…

A:

Q: of the above answers is correct. 21. If A and B are not-mutually exclusive events, then: cannot…

A:

Q: : If A, B, C are mutually independent events then A UB and C are also independent.

A: Answer: For the given data,

Q: When two events cannot occur at the same time, they are said to be ?

A: Disjoint events:   Let A and B be any two events, if the events A and B are mutually exclusive or…

Q: 1. Which event is illustrated in the Venn diagram below? A OO P(A or B) A. Dependent Event B. Not…

A: As per our guidelines we can solve first multiple-choice question and rest can be reposted.…

Q: Suppose A and B are events such that P(A) = 0.6 P(B)= 0.7 and P(A or B) = 0.8 What’s P(A) with a…

A: Given, Suppose A and B are events such that P(A) = 0.6 P(B)= 0.7 and P(A or B) = 0.8. That is,…

Q: Suppose that C and D are mutually exclusive events such that P(C) = 0.14 and P(D) = 0.32. Determine…

A: Given, P(C) = 0.14  P(D) = 0.32  P(C or D)=?

Q: If A & B are two events and p(B) ≠ 1, prove that p(A/B') = [p(A) - p(A∩B)/[1 - p(B) where B'…

A: We have, two events A and B thus,  P(A|B')=P(A∩B')P(B')          ......(1)We know that,…

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

A:

Q: Suppose that a family is leaving on a summer vacation in their camper and that M is the event that…

A: Note: Hey, since there are multiple subparts posted, we will answer first three subparts. If you…

Q: In the experiment of rolling a pair of dice, the events A, B and C are defined as A: getting 2 on…

A: Given that In the experiment of rolling a pair of dice, the events A, B and C are defined as A:…

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: Suppose that the events A, B and C are mutually independent with  P(A) = 1/2 , P(B) = 1/3, P(C) =…

A: Given A,B, and C are mutually independent P(A) = 1/2 P(B) = 1/3 P(C) =  1/4

Q: Suppose a coin is tossed thrice. Let the event A be "getting three heads" and B be the event of…

A:

Q: Suppose three events namely A1, A2, and A3. Show that P(A, U A, U A, ) = P(A,)+ P(A,)+ P(A,) iff…

A:

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

A:

Q: An experiment consists of picking one of two urns at random and then selecting a ball from the urn…

A: An experiment consists of picking one of two urns at random and then selecting a ball from the urn…

Q: Which pair(s) of events are Mutually Exclusive.

A: In a competition, two people will be selected from four finalists to receive first prize and second…