This exercise allows practice of the TREE DIAGRAMS useful in Conditional Probability computations. In this exercise, the tree diagram is constructed for events A, B, C, X, and Y.   (a) What is P(B)?  (b) What is P(X|B)?  (c) What is P(X AND B)?  (d) What is P(X)?  (e) What is P(B|X)?  (Please be sure to note this is NOT the same as P(X|B)) (IN THIS EXERCISE ALONE, ROUND YOUR FINAL ANSWER TO THREE DECIMAL PLACES) (f) Based on your computations, are events B and X independent events?

Q: Which pairs of events are independent?     (a) P(A) = 0.67, P(B) = 0.58, P(A∩B) = 0.35.         A…

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Q: Suppose events A, B, and Care independent and PLA) - PIB) - PC) - Find the probability. (Enter the…

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Q: When 2 events (A,B) are independent, what is the probability of their union? a.) P(A) + P(B) b.)…

A: Let us consider two events A and B.   Consider A and B are independent events.

Q: Which of the following is NOT necessarily true for mutually exclusive events A and B? P(A B)=0…

A: If A and B are mutually exclusive events, then A∩B=∅. Then, we have P(A∩B)=P(AB)=0. 1.)…

Q: What are properties that only, independent events have? Select all. P(AN B) P(B) P(A| B) O P(A| B) =…

A: The two events are said to be independent if occurrence of one event doesn't depend on the…

Q: c. Give an example of events A, B, and C such that P(ANBNC) = P(A)P(B)P(C), but PĀNBNT) ‡…

A: The  events are  A B C P(A∩B∩C) = P(A)P(B)P(C)butPA¯∩B¯∩C ≠P(A¯)P(B¯)P(C¯)

Q: q10- Two events A and B are said to be independent if: Select one: a. P(A ∩ B)= P(A)*P(B) b. All…

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Q: We saw that we can use inclusion-exclusion with conditional probabilities of the form P (AUB|C). Can…

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Q: (a) Find the probabilities of the events below. Write each answer as a single frection. P(4) - P(B)…

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Q: Supposed P(F) = .25, P(F or G) = .70, and events F and G are mutually exclusive.  Find: a) P(G)…

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

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…

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Q: Which of the following expressions must be true if events A and B are independent? Choose from the…

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Q: NUMBER OF COMPUTERS SOLD PROBABILITY X-P(X) (X-) (X-2-P(X) P(X) 0.1 (1) (6) (11) (16) 1 0.2 (2) (7)…

A: The following incomplete table is given: x P(X) X.P(X) X-μ X-μ2 X-μ2.P(X) 0 0.1         1…

Q: If A and B are independent events, which of the statements below are true? OP(AIB)-0 O P(AIB)-…

A: From the given information we find the probability.

Q: Which of the following is a benefit of having replication in the experiment? Repeating the…

A: n(sample size for new style golf balls)=40 m(sample size for original style golf balls)=40

Q: B) are disjoint, what is the probability of their union? a.) P(A) + P(B) b.) P(A)P(B) c.) 0 d.)…

A: As given that events A and event B are disjoint. It is asked to find the probability of their union.

Q: The table displays the number and type of tickets bought for a baseball tournament held on a…

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Q: We are asked to find the probability of event A occurring given that event B occurs. This is…

A: By conditional probability theorem, the probability of event A occurs, provided that the event B has…

Q: Let the events A and B be Such that PrAC) = to +10)%, PIB)= (8+15)%. Find P (AUB), if 1= A and B are…

A: If A and B denote two events, the probability PA∪B denotes the probability of either of the events…

Q: Consider the notation: P(E∣F)P(E∣F) Which event do we have knowledge of having already occurred?

A: The conditional probability is as below: PA|B=PA∩BPB

Q: True or False: for each of the following statements, decide if it is true or false. If it is rue,…

A: As per given by the question, there are two statement are given and find whether the statement true…

Q: Use the diagram to find the probabilities below. (a)    P(A) (b)    P(E | A) (c)    P(A E)

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

Q: P(E | FC )   (b)    P(F | EC )

A: The probability that the only event E is occurs is, PE∩FC=PE-PE∩F=0.25-0.15=0.10 The probability…

Q: a) Show that for any three events A, B, and C, the probability that at least one of them occurs is…

A: Given  We need to prove that for three events A,B and C,the probability that atleast one of them…

Q: On an airplane, 92% of people are in economy seats (also known as coach.) Of the people in economy,…

A: given data  event E : in an economy seatevent F : member of frequent flierP(in an economy seat) =…

Q: By rewriting the formula for the Multiplication Rule, you can write formula for finding conditional…

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Q: The addition Rule: P(A or B) = P(A) + P(B) - P(A and B) A useful formula: P(A and B) = P(A)*P(B)…

A: It is given that, P(A or B) = 0.253, P(A) = 0.208 and P(A and B) = 0.509.

Q: The general multiplication rule says that P(A and B)=_______If A and B are events, the…

A: Here given , The general multiplication ,  multiplication rule  P(A and B) = P(A). P(B).

Q: 30 P(B)= 100 40 P(B| A) = 100 25 The events A, B and C are given such that P(A)= 30 20 and P(AOBOC)…

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Q: Show that the probability of the union of (non-mutually exclusive) events A and B can be written as…

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Q: Finite: If A and B are events such that P(A)=0.5 and ​P(A∪​B)=0.9​, find​ P(B) when ​(a) A and B…

A: Given that, Let A and B are events such that P(A)=0.5 and ​P(A∪​B)=0.9

Q: Determine if events [A] and [B] are independe P(A) - P(B)- 3 P(A and B) 10 3 25 Answer: 1 P(A and B)…

A: if events [A] and [b] are independentP(A and B)=P(A).P(B)

Q: Researchers at a drug company are testing the duration of a new pain reliever. The drug is normally…

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Q: Find P(A|B) if A is a subset of B.

A: The formula of the conditional probability is,      Subset of the event means the every outcomes of…

Q: The events A and B are such that ?(?) = 4/9?(?|?) = 1/2?(? ∪ ?) = 2/3 (i) Draw a Venn diagram to…

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Q: For two events A and B, P(A)=0.24, P(B)=0.57, and P(A∩B)=0.32. a.Find P(A|B) b. Find P(B|A) c.…

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Q: For each set of probabilities, determine whether the events A and B are independent or dependent.…

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Q: By rewriting the formula for the Multiplication Rule, you can write a formula for finding…

A: Given the formula for the conditional probability of evet B occurring given that event A has…

Q: April has a bag with 7 blue sweets and 3 red sweets  in it She picks up a sweet at random from the…

A: The number of blue sweets in the bagThe number of red sweets in the bagThe total number of sweets,

Q: P(A) = 0.4 and P(B) = 0.5. Complete parts (a) through (d). Suppose that events A and B are disjoint,…

A: According to the given information in this questionThere are more than three subparts according to…

Q: Suppose that we have a deck of 30 cards. Both sides of the first 10 cards are colored red, both…

A: Given: Let R be the event that the top side of the top card is red.Let B be the event that the…

Q: Find each probability by referring to the tree diagram above. (a)   P(C|A)=P(C|A)=  (b)…

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Q: In example,  A and B are two independent events with P (A) = 0.50 and P (B) = 0.20. Count it for  P…

A: P(A) and P(B) = P(A x B) Thus P(A×B)=0.50×0.20=0.1