If two events are mutually exclusive, then the following is true: a. They cannot be mutually exclusive. b. The events may occur concurrently. c. They could also be complementary. d. They are independent.
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…
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A: Mutually Exclusive events: Events which cannot occurs together are called mutually exclusive events.…
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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…
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Q: If A, B are mutually exclusive events, then the probability that A does NOT occur given that B…
A: if A and B are mutually exclusive events then A∩B=∅ i.e. P( A∩B)=0 let A¯ is complement of A. now,…
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Q: 1. True or False. (A) If events A and B are independent, then they are also mutually exclusive (B)…
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Q: If the outcome of event A is not affected by event B, then events A and B are said to be mutually…
A: Independence condition: If A and B are independent events, then P(A and B)=P(A)*P(B). That is,…
Q: If events A and B are mutually exclusive, and P(A) = 0.7, P(B) = 0.2, then the P(AUB) = ? O a. 0.72…
A: From the provided information, P (A) = 0.7 and P (B) = 0.2 Events A and B are mutually exclusive.
Q: Select one: a. The events A and B are not mutually exclusive. b. None of the above. c. The…
A: It is an application of set theory . It forms a basic fact of probability .
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Q: If A and B are mutually exclusive events, then P(A U B) equals А.Р(A)+P(B)-P(Ав) В.Р(А)xP(В)
A: Given,if A and B are mutually exclusive events .so, P(A∩B)=0
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Q: Let ? and ? be two mutually exclusive events. Given that (?)=0.25 and ?(?∪?) =0.77, determine ?(?).
A: Given: P(A)=0.25 P(A∪B)=0.77
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 P(A∪B)=0.6, P(A)=0.4, and P(A∩B)=0.25, find P(B). Assume that A and B are events.…
A: GivenA and B are eventsP(A∪B)=0.6P(A)=0.4P(A∩B)=0.25
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Q: If A and B are independent events. Then A and BC are independent.
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Q: I. The events A and B are mutually exclusive. If P(A) = 0.1 and P(B) = 0.3 , what is P(A or B)? II.…
A: 1)i)Events A and B are mutually exclusiveP(A)=0.1P(B)=0.3
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A: Given A card is drawn from a pack of 52 cards so that each card is equally to be selected.
Q: equals
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- For each of these problems, you need to a) translate each sentence into probability notation, then b) determine if the specified events are independent. You must show work for independence. 1. The probability that a person plays on a high school basketball team is .031. The probability that a person plays on a high school baseball team is .04. The probability that a person plays on a high school baseball team and a high school basketball team is .017. Determine if the events "plays on a high school basketball team" and "plays on a high school baseball team" are independent events. 2. The probability that a person likes the superhero Iron Man is .46. The probability that a person likes the superhero Captain America is .58. The probability that a person likes the superhero Captain America given that the person likes the superhero Iron Man is .46. Determine if the events "likes Iron Man" and "likes Captain America" are independent events. 3. The probability that a person likes the…An experiment consists of rolling a fair die twice. Let A be the event that in the second roll the die lands 1, 2, or 5; B be the event that in the second roll the die lands 4, 5, or 6; and C be the event that the sum of the two outcomes from the two rolls is 9. Please choose the correct answer:12. Give the equations that represent each situation. For Independent Events: P(AN B) = P(AU B) =, For Mutually Exclusive Events: P(AN B) = P(AU B) = For Dependent Events: P(AN B) = P(A U B) =
- Suppose we have events A, B, and C with probabilities: P ( A ) = 0.4 , P ( B ) = 0.2 , P ( C ) = 0.3. We also know that: A and B are independent, A and C are mutually exclusive, and P ( B ∩ C ) = 0.15 Compute each of the following. Write your answers as decimals. P ( A ∩ B ) = P ( A ∪ B ) = P ( B ∪ C ′ ) =If A and B are events which are conditionally independent given a third event C, which of the following is not necessarily true? Select one: O a. P(An B|Cº) = 1 – P(A|C)P(B|C) O b. P(BANC) = P(B|C) O c. None of the other choices d. P(An B|C) = P(A|C) – P(A|C)P(Bª|C) O e. P(An BnC) = P(A|C)P(BC)Which of the following statements is false? Two independent events cannot occur at the same time. Two complementary events cannot occur at the same time. Two disjoint events cannot occur at the same time.
- Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.On Mr. Casper's debate team at Thunderbird High School, 20% of the members are Sophomores, 35% are Juniors and 45% are Seniors. A team member is selected randomly to give the closing argument for the team. If a sophomore gives the closing argument, the team has a probability of 0.25 of winning the debate. If a junior gives the closing argument, the probability of winning is 0.6. If a senior closes, the probability of winning is 0.85. (a) Find the probability that the team wins the debate. b sketch a tree diagram to model this processIJ A and B are independent events, prove that the events A and B, A and B; and A and B are also independent.
- Suppose that in a large university, 40% of students work part time, 10% are part of one of the university's sports teams, and 5% both work part time and are part of one of the university's sports teams. Let W be the event that a student works part time, and V be the event that a student is part of one of the university's sports teams. Make sure all your answers are expressed in terms of the events W and V,. 4. А. What is the probability that a randomly selected student works part time or is a part of one of the university's sports teams? В. teams? What proportion of students do not work part time but are part of one of the university's sports С. Are W and V independent events? D. If a student works part time, what is the probability they are also part of one of the university's sports teams? Е. What proportion of students are not part of any of the university's sports teams and work part time?Suppose there are exactly three states of weather: sunny, cloudy, or rainy. If it is sunny today, then the probability is 3/4 that it will be sunny tomorrow, 1/8 that it will be cloudy tomorrow, and 1/8 that it will be rainy. If it is cloudy today, then the probability is 1/2 that it will be sunny tomorrow, 1/4 that it will be cloudy tomorrow, and 1/4 that it will be rainy. If it is rainy today, then the probability is 1/4 that it will be sunny tomorrow, 1/2 that it will be cloudy tomorrow, and 1/4 that it will be rainy. cloudy is From this Markov model, for any given day the probability that it will be sunny is rainy is Round your answers to three decimal places. andA favorite casino game of dice “craps” is played in the following manner: A player starts by rolling a pair of balanced dice. If the roll (the sum of two numbers showing on the dice) results in a 7 or 11, the player wins. If the roll results in a 2 or 3 (called “craps”) the player loses. For any other roll outcome, the player continues to throw the dice until the original roll outcome recurs (in which case the player wins) or until a 7 occurs (in which case the player loses). When answering the following questions, you can use this outcome chart for the roll of two dice: Provide the probability answers in fraction and in decimal forms rounded to 4 digits. A. List the possible outcomes (sample space) for winning on the first roll of the dice. B. What is the probability that a player wins the game on the first roll of the dice? C. List the possible outcomes (sample space) for losing on the first roll of the dice. D. What is the probability that a player loses the game on the…
