Let ? and ? be two events. a) If the events ? and ? are mutually exclusive, are ? and ? always independent? If the answer is no, can they ever be independent? Explain. b) If ? ⊂ ?, can ? and ? ever be independent events? Explain.

Q: f we define an event a, then there is an event NOT A, that is also called A.  The supplement of A.…

A: The complement of any event A is the event (not A) i.e., the event A does not occur. The vent A and…

Q: Let S = {2, 7, 12, 17, 22, 27}, E = {7, 17, 27}, F = {2, 12, 22},and G = {22, 27}. (Enter ∅ for the…

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Q: A class with n kids lines up for recess. The order in which the kids line up is random with each…

A: J represents John B represents Betty M represents Mary.

Q: | P(An B) = ? a. {HH,TH} |B' = ? b. {HT, ТH} v A' ? с. 0.25 | P(AU B) = ? ]P(A) = P(B) = ? d. 0.75…

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Q: You roll a die. If you roll less than 6, you get to draw one raffle ticket out of a basket with 100…

A: Given that  A = you win the grand prize and B = You roll a 6. There are 6 sides on a die. So the…

Q: Determine

A: Here use dependent and independent event

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A: From the given information we find the probability.

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A: Here, given that  a box contains 40 blocks. For each of the colors red, blue, green, or yellow there…

Q: QUESTION 1 If two events A and 8 are mutually exclusive then: O a. P(AJ + P(B) = 1 O b.A and 8 are…

A: 1. We know if, A and B events are mutually exclusive then, P(A U B) = P(A)+P(B) Now, we know, P(A U…

Q: Since events A and B are independent events; Prove that the events depicted in the picture are…

A: Given that the events A and B are independent events.

Q: Event C is defined as the set of positive even integers; Event E is defined as the set of odd…

A: Mutually Exclusive Events: Another name of Mutually exclusive events is Disjoint events. An event is…

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

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Q: A class with n kids lines up for recess. The order in which the kids line up is random with each…

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Q: Let S = {5, 10, 15, 20, 25, 30}, E = {10, 20, 30}, F = {5, 15, 25}, and G = {25, 30}. (Enter ∅ for…

A: The answer is mentioned below

Q: Assume that a student is chosen at a random from a class. Determine whether the events eight and B…

A: The given data is as follows:Event A: the student is a womanEvent B: the student belongs to its…

Q: if $A$ and $B$ are events, then $\Pr[A\cap B]\geq \Pr[A]+\Pr[B]-1$

A:

Q: Define event A as students in the IE department; event as students who is working on thesis in the…

A: We have to define event and check statement is true or false for mutually exclusive events.

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A: If the two events do not occur same time then it is called as mutually exclusive events.

Q: A class with n kids lines up for recess. The order in which the kids line up is random with each…

A:

Q: A blue die and a red die are thrown. B is the event that the blue comes up with a 6. E is the event…

A: E ∩ B means E and B, this means blue comes up with a 6 and sum of the dice is 8. This can only…

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

A: Answer: For the given data,

Q: If A and B are independent events. Then A and BC are independent.

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Q: In a survey, respondents were asked to indicate their favorite brand of cereal. They were only…

A: Independent events : Occurrence of one does not affect probability of occurrence of other event…

Q: Suppose we are interested in the pairwise intersection. What is the pairwise intersection for the…

A: (5)Explanation:In the given, we can determine the pairwise intersection for events E and F by…

Q: Let S = {4, 9, 14, 19, 24, 29}, E = {9, 19, 29}, F = {4, 14, 24}, and G = {24, 29}. (Enter ∅ for the…

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Q: Select all of the events that would be considered to be mutually exclusive events. O male and female…

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Q: A cell phone salesperson has kept records on the customers who visited his store. Forty percent of…

A: Given information: 40% of the customers who visited the store were female. 35% of the females who…