We have two events, A and B. P(A) = 1/2 and P(B) = 1/3. Hint: Draw Venn diagrams to help you think about the following possibilities: 1) if A and B are mutually exclusive, 2) if all the outcomes in B are also in A, 3) if there’s partial but not complete overlap between events in A and events in B. (a) What is the smallest P(A and B) can be? _________ (b) What is the largest P(A and B) can be? _________ (c) What is the smallest P(A or B) can be? _________ (d) What is the largest P(A or B) can be? _________

Q: 10. Suppose a student is selected at random from a large college population. a. Label each pair of…

A: Correct option is B. EXPLANATION : Mutually exclusive events : Two events are said to be mutually…

Q: Two fair (six-sided) dice are rolled, one blue and one red. Let A: "Sum of 8", and let B: "Red die…

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Q: Consider two events A and B. Suppose P (A ∪ B) = 0.7 and P (A ∪ B′) = 0.9. Find P (A) (a Venn…

A: The given data for events A and B is(A  B) = 0.7 and P (A  B′) = 0.9

Q: . You look at a process that has three activities; each one can potentially go wrong. Howmany leaves…

A: The process has three activities. The activity can be wrong or right. So, the possible outcomes are…

Q: 2) Suppose A and B are events such that P(A) = 0.6, P(B) = 0.7 and P(A or B) = 0.8. Calculate the…

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

Q: 4. Suppose an individual is randomly selected from the population of all adult males living in the…

A: Introduction: It is required to compare the probabilities, P (A | B) and P (B | A)  in the given…

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…

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Q: 11. Given two events, A and B. Find the following if P(A)=0.7, P(B)=0.5, and P(A U B)=0.9. Complete…

A: Given: P(A) = 0.7 P(B) = 0.5 P(AUB) = 0.9 Formula Used: P(A∩B) = P(A)+P(B)-P(A∪B) P(A∪B)' = 1-P(A∪B)…

Q: Given two events A and B , state whether each of the following can be possible or not  a) P(A) P(A)…

A: The union of two events is the occurrence of either of them or at least one of them. The…

Q: 1. Given two events, A and B. Find the following if P(A)=0.7, P(B)=0.5, and P(A U B)=0.9. Complete a…

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Q: 5. We have two events, A and B. P(A) = 1/2 and P(B) = 1/3. Hint: Draw Venn diagrams to help you…

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Q: This problem is to show that determining if two events are independent is not always obvious. 1.…

A: A family of three children :  N(S) = 23 = 8 possible combinations  Total S=…

Q: 8. Two events, A and B, are such that P(A)=.45,P(B) = .65,Pl B)=.25, determine PBN

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Q: 5. Bayes' theorem for an 'AND’ combined event is: Pr( A 'AND’ B) = Pr( A|B )*Pr( B ). When does this…

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Q: 13 13 2. (222) = 2 · (¹12) ² 2 4 Problem 3. Two events A and B are such that P(A) = 0.4, P(B) = 0.3,…

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Q: 4. Events A and B are such that P(A) =P(A|B) =,P(B) = a) Find P(B|A) b) Find P(BnA) c) Are events A…

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Q: Complete the following table and use it calculate the probabilities given below. A AC Total a. PA or…

A: Given data is:   B Bc Total A 0.443 0.218   Ac       Total 0.567   1

Q: 5. Let E and F be two events in an experiment. (a) Explain, using a Venn diagram, why (b) Explain…

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Q: Two events A and B are such that P(A)=0.25, P(B)=0.4, and P(AUB)=0.5. Draw a Venn diagram to…

A: Venn diagram is the diagrammatic representation of the different sets. If there is a common in the…

Q: Question 1. Suppose A and B are events with P(A) = ½, P(B) and 113 P(A or B) = a) Are A and B…

A: Given that  P(A) = 1/3 , P(B) = 1/4 , P(A or B) = 1/2

Q: 13. Suppose that E and F are two events and that P(E)= 0.6 and P(F|E) = 0.7. What is P(E and F)? P(E…

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Q: 6a. Supposed P(A) = .45, P(B) = .24, and events A and B are mutually exclusive. Find... a. P(A or…

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Q: 2. Two events A and B are mutually exclusive with probability (A)=0.5 and probability (B)=0.4 Find…

A: Given: A and B are mutually exclusive events.

Q: An event that cannot be defined in terms of more basic outcomes is called a

A: Event is the outcome of a random experiment. For example, the occurrence of head atleast once in 2…

Q: 3.8. Let A, B, and C be events relating to the experiment of rolling a pair of dice. a. If P(AC) >…

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