Suppose we have three events A, B, and C. If P(A) > 0, P(B) > 0 and P(C) < 1, and we know that if both A and B occur, then C must occur. Show that A, B and C are not mutually independent.
Q: n each of the cases, briefly state whether the 2 events A and B are indpendent and why (a) Roll two…
A: a. If two dice are rolled then total number of outcomes 6*6 = 36 Define two events, A: The first die…
Q: A woman decides to have children until she has her first girl or until she has four children,…
A: The objective of the question is to find the probability of each simple event in the sample space…
Q: What is the probability that all three components function properly throughout the warranty period?…
A: As per bartleby guidelines we can solve only first three subparts and rest can be reposted
Q: Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a…
A:
Q: Tom, Mike and Jane decode the code independently, the probabilities of their successfully decoding…
A: Here, given that three people decide the code independently and the probabilities of each event is…
Q: A family has three children, eacher of whom is a boy or a girl with probability 1/2. Let A = "there…
A: (a). Ans :- A and B are independent. Explanation :- Given that, The family has 3 childrens. i.e…
Q: An event A occurs with probability 0.4. Event B occurs with probability 0.2. If A and B are…
A:
Q: 3. A system comprised of three independent components. The probability of failure for each component…
A: Three independent components. Probability for failure for 1st component : p1=0.1 P2=0.2 P3=0.3
Q: Suppose that Albert and Leo are in a contract dispute. Leo has breached their contract and this has…
A: Given Albert and Leo are in dispute.The court cost for each of them if they go to trial =$1000 X be…
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: Are events Q and S independent events?
A: ALASKA INVESTMENT CORP has decided to choose two of a group of three utility stocks. Suppose we…
Q: Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a…
A: Given that, A1 be the event that the receiver functions properly throughout the warranty period, A₂…
Q: nt Xc [] Event X intersection Y [] Event X union Y [] Event X union Yc 2. True or false The…
A: The possible events are the events which cannot occur at any performance of the experiment. If one…
Q: ALASKA INVESTMENT CORP has decided to choose two of a group of three utility stocks. Suppose we…
A:
Q: This student never eats the same kind of food for 2 consecutive weeks. If she eats a Chinese…
A: From the given information, The student never eats the same kind of food for 2 consecutive weeks.…
Q: Shannon owns two stocks: A and B. The probability that A will be profitable is 0.7. The probability…
A:
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,…
Q: 1. True or False. (A) If events A and B are independent, then they are also mutually exclusive (B)…
A:
Q: An office has 2 fire detectors. Suppose that 3 out of every 100 fire detectors will fail to go off…
A: It is given that, 3 out of every 100 fire detectors will fail to go off during a fire.
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: Q3. Suppose three students of NSU named A, B and C are going to sit their spring semester final exam…
A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…
Q: If two events A and B have the same (non-zero) probability... Group of answer choices the two…
A: The given information is:The given statement is:"Two events and have the same (non-zero)…
Q: Suppose that A,B, & C are three independent events such that Pr(A)=1/4, Pr(B)=1/3, and Pr(C)=1/2. A.…
A:
Q: Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a…
A:
Q: . Suppose 2 doctors A and B test all patients coming into a clinic for Syphilis. Let A+ = {doctor A…
A: The proportion of patients diagnosed positive by doctor A = 0.10 The proportion of patients…
Q: A fair coin is flipped 4 times. If X and Y are the number of heads and tails obtained, respectively,…
A:
Q: 3) Let us assume that we have a five sided die. The sides of the die are marked with the numbers –2,…
A: The distribution of X is given Let us compute E(X2) E(X2)=∑xx2P(X=x)=(-2)2 P(X=-2)…
Q: The printing machine consists of three parts A, B, C. The Probability of part A failure is 0.1. The…
A: Given,
Q: Let's say (B₁, B₂, B3, B4, B5) is a collection of events that are mutually exclusive events. If…
A: Two events are said to be mutually exclusive if both of them cannot occur at the same time. Two…
Q: : If A, B, C are mutually independent events then A UB and C are also independent.
A: Answer: For the given data,
Q: This student never eats the same kind of food for 2 consecutive weeks. If she eats a Chinese…
A: If X(t), t∈T is a stochastic process such that, given the value X(s), the value of X(t), t>s, do…
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
Q: One coin is tossed twice. Case A is the first shot coming in tails, case B is the second shot coming…
A: It was stated that a coin is tossed twice. Case A is the first shot coming in tails. case B is the…
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
Q: This student never eats the same kind of food for 2 consecutive weeks. If she eats in a Korean…
A: Let us assume State 1 is Korean, State 2 is Turkish, State 3 is French. So, the first column…
Q: Suppose you have three bowls, X, Y , and Z with some number of red and blue balls. Bowl X has 2 red…
A:
Step by step
Solved in 2 steps with 2 images
- This student never eats the same kind of food for 2 consecutive weeks. If she eats a Chinese restaurant one week, then she is equally likely to have Greek as Italian food the next week. If she eats a Greek restaurant one week, then she is three times as likely to have Chinese as Italian food the next week. If she eats a Italian restaurant one week, then she is four times as likely to have Chinese as Greek food the next week. Assume that state 1 is Chinese and that state 2 is Greek, and state 3 is Italian. Find the transition matrix for this Markov process. P =This student never eats the same kind of food for 2 consecutive weeks. If she eats a Chinese restaurant one week, then she is five times as likely to have Greek as Italian food the next week. If she eats a Greek restaurant one week, then she is four times as likely to have Chinese as Italian food the next week. If she eats a Italian restaurant one week, then she is twice as likely to have Chinese as Greek food the next week. Assume that state 1 is Chinese and that state 2 is Greek, and state 3 is Italian. Find the transition matrix for this Markov process. P = 出 出 曲n = {1, 2, 3, 4} with each point carrying probability 1/4. Let A1 = {1, 2}, A2 = {1, 3}, A3 = {1, 4}. Then any two of A1, A2, A3 are independent, but A 1 , A 2, A 3 are not independen
- Four apples and four oranges are distributed between two boxes in such a way that each of them has four fruits. At each step, we withdraw one fruit from each box and exchange them. Let Xn be the number of apples in the first box. Find the limiting probabilities.Help in mrakov models. First 3 sub questionsYou are the teacher of two math classes of 20 and 25 students respectively. To get into a university program, the students need a 75% in the class. Suppose each student has a 0.7 probability of getting atleast a 75% in the class. Let X1 be the number of students in the class of 20 who receive atleast a 75%. Let X2 be the number of students in the class of 25 who receive atleast a 75%. a. Do X1 and X2 fit the binomial setting? Are there any issues? For the rest of the question, assume both X1 and X2 can be modeled by a binomial distri- bution. b. What is the probability that exactly 15 students in the class of 20 get into the pro- gram? Do not use Table C. c. What is the probability that atleast 22 students in the class of 25 get into the pro- gram? Do not use Table C. d. Using Table C, what is the probability that atleast 17 students in the class of 20 get into the program? е. Let X be the number of students in both classes that get into the program. Deter- mine the mean and standard…
- IJ A and B are independent events, prove that the events A and B, A and B; and A and B are also independent.Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let A₁ be the event that the receiver functions properly throughout the warranty period, A₂ be the event that the speakers function properly throughout the warranty period, and A3 be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P(A₁) = 0.92, P(A₂) = 0.96, and P(A3) = 0.90. (Round your answers to four decimal places.) (a) What is the probability that all three components function properly throughout the warranty period? (b) What is the probability that at least one component needs service during the warranty period? (c) What is the probability that all three components need service during the warranty period? (d) What is the probability that only the receiver needs service during the warranty period? (e) What is the probability that exactly one of the three components needs service…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…If the student attends class on a certain Friday, then he is five times as likely to be absent the next Friday as to attend. If the student is absent on a certain Friday, then he is three times as likely to attend class the next Friday as to be absent again.