Hello i need this to be solved for me pls because i am preparing for exam at the moment and i dont know wat to do

MAT 281 EXERCISES 1. Two students are randomly selected from a statistics class, and it is observed whether or not they suffer from math anxiety. How many total outcomes are possible? Draw a tree diagram for this experiment. Draw a Venn diagram. 2. In a large city in Cyprus, 15,000 workers lost their jobs this year. Of them, 8300 lost their jobs because their companies closed down or moved, 3100 lost their jobs due to insufficient work, and the remainder lost their positions because their positions were abolished. If one of these 15,000 workers selected at random, find the probability that this worker lost his or her job i. Because the company closed down or moved ii. Due to insufficient work iii. Because the position was abolished iv. Do these probabilities add up to 1.0? If so, why? 3 In a sample of 500 families from Nigeria, 80 have a yearly income of less than 40,000 dollars, 240 have a yearly income of 40,000 to 80,000 dollars, and the remaining families have a yearly income of more than 80,000 dollars. Write the frequency distribution table for this problem. Calculate the relative frequencies for all classes. Suppose one family is randomly selected from these 500 families. Find the probability that this family has a yearly income of i. Less than 40,000 dollars ii. More than 80,000 dollars 4 A statistical experiment has eight equally likely outcomes that are denoted by 1, 2, 3, 4, 5, 6, 7, and 8. Let the event = {2, 5, 7} = {1, 5, 8} i. Are events A and B mutually exclusive? ii. Are events A and B independent events? iii. What are the complements of A and B and their respective probabilities? 5 There a total of 150 practicing Physicians in a city in Syria. Of them, 70 are female and 20 are pediatricians. Of the 70 females, 10 are pediatricians. Are the events \"female\" and \"pediatrician\" independent? Are they mutually exclusive? Explain why or why not. 6 Five hundred employees were selected from Iraq's large private companies, and they were asked whether or not they have any retirement benefits provided by their companies. Based on this information the following two-way classification table was prepared Have retirement benefits Yes Men 240 Women 135 No 60 65 a. If one employee is selected at random from these 500 employees, find the probability that this employee i. A woman ii. Has retirement benefits iii. Has retirement benefits given the employee is a man iv. Is a woman given that she does not have retirement benefits b. Are the events \"man\" and \"yes\" mutually exclusive? What about the events \"yes\" and \"no\"? Why or why not? c. Are the events \"woman\" and \"yes\" independent? Why or why not? 7 Find the joint probability of A and B for the following. a. () = 0.59 (|) = 0.81 b. () = 0.31 (|) = 0.35 8 The following table gives a two-way classification of all basketball players at a state university in Turkey who began their college careers between 2004 and 2008, based on gender and whether or not they graduated. Graduated Male 126 Female 133 Did Not Graduate 55 32 a. If one of these players is selected at random, find the following probabilities. i. ( ) ii. ( ) iii. Find ( ). Justify your answer. 9 Find ( ) for the following i. () = 0.66, () = 0.47 ( ) = 0.33 ii. () = 0.92, () = 0.78 ( ) = 0.65 10 A ski patrol unit in Zimbabwe has nine members available for duty, and two of them are to be sent to rescue an injured skier. In how many ways can two of these nine members be selected? Now suppose the order of selection is important. How many arrangements are possible in this case? 11 A company in Sudan employs a total of 16 workers. The management has asked employees to select 2 workers who will negotiate a new contract with management. The employees have decided to select the 2 workers randomly. How many total selections are possible? Considering that the order of selection is important, find the number of permutations. 12 A player in Ankara plays a roulette game in a casino by betting on a single number each time. Because the wheel has 38 numbers, the probability that the player will win in a single play is 1/38. Note that each play of the game is independent of all previous plays i. Find the probability that the player will win for the first time on the 5 th play. ii. Find the probability that it takes the player more than 80 plays to win for the first time iii. The gambler claims that because he has 1 chance in 38 of winning each time he plays, he is certain to win at least once if he plays 38 times. Does this sound reasonable to you? Find the probability that he will win at least once in 38 plays. 13 A screening test for a certain disease is prone to giving false positives or false negatives. If a patient being tested has the disease, the probability that the test indicates a (false) negative is 0.14. If the patient does not have the disease, the probability that the test indicates a (false) positive. Is 0.08. Assume that 3% of the patients being tested actually have the disease. Suppose that one patient is chosen at random and tested. Find the probability that a. This patient has the disease and test positive b. The patient does not have the disease and tests positive c. This patient tests positive d. The patient has the disease given that he or she tests positive 14 The following table gives the probability distribution of a discrete random variable . 0 1 2 3 4 5 () 0.05 0.19 0.28 0.31 0.12 0.05 Find the following probabilities a. ( = 1) b. ( 1) c. ( 3) d. (0 2) b. Probability that a value less than 3 c. Probability that a value greater than 3 d. Probability that a value in the interval 2 to 4 e. Calculate the mean (expected value) of the probability distribution f. Find the variance and standard deviation 15 Let be a discrete random variable that possesses a binomial distribution. Using the binomial formula, find the following probabilities a. ( = 0) = 4 = 0.01 b. ( = 4) = 7 = 0.80 c. ( = 7) = 8 = 0.60 Verify your answers using the binomial distribution table 16 A professional basketball player from Nigeria makes 85% of the free throws he tries. Assuming this percentage will hold true for future attempts, find the probability that in the next six tries, the number of free throws he will make is a. Exactly 6 b. exactly 4 c. at least 4 17 An office supply company in Sana'a (capital of Yemen), conducted a survey before marketing a new paper shredder designed for home use. In the survey, 80% of the people who used the shredder were satisfied with it. Because of this high acceptance rate, the company decided to market the new shredder. Assume that 80% of all people who will use it will be satisfied. On a certain day, seven customers bought this shredder. a. Let denote the number customers in this sample who will be satisfied with this shredder. Use binomial distribution to obtain the probability distribution of . Find the mean, variance and standard deviation of . b. Using the probability distribution of part a, find the probability that exactly four of the seven customers will be satisfied. 18 Magnetic resonance imaging (MRI) is a process that produces internal body images using a strong magnetic field. Some patients become claustrophobic and require sedation because they are required to lie within a small, enclosed space during the MRI test. Suppose that 25% of all patients undergoing MRI testing require sedation due to claustrophobia. If five patients are selected at random, find the probability that the number of patients in these five who require sedation is a. Exactly 2 b. all 5 c. exactly 4 19 A commuter airline in Libya, receives an average of 9.7 complaints per day from its passengers. Using the Poisson formula, find the probability that on a certain day this airline will receive exactly 5 complaints. 20 An average of 0.6 accidents occurs per day in a particular city in Kenya. a. Find the probability that no accident will occur in this city on a given day. b. Let denote the number of accidents that will occur in this city on a given day. Write the probability distribution of . c. Find the mean, variance, and standard deviation of the probability distribution developed in b. 21 A high school basketball team in Saudi Arabia averages 1.2 technical fouls per game. a. Using the appropriate formula, find the probability that in a given basketball game this team will commit exactly 3 technical fouls. b. Let denote the number of technical fouls that this team will commit during a given basketball game, write the probability distribution of . ADVANCED EXERCISES 1 1. The probability that any child in a family will have blue eyes is 4 .This feature is inherited independently by different children in the family. If there are 5 children in the family and it is known that at least one of these children has blue eyes a. What is the probability that at least 3 of the children have blue eyes? b. If it is known that the youngest child in the family has blue eyes, what is the probability that at least 3 of the children have blue eyes? c. Explain why the answer in part (a) is different from the answer in part (b). 2. A bag contains 1 White ball and 2 Red balls. A ball is drawn at random. If the ball is White, it is replaced in the bag with 1 extra White ball. If the ball is Red, it is replaced in the bag with 2 extra Red balls. A second ball is then drawn at random. a. What is the probability that the second ball is Red? b. Suppose that the result of the first draw is unknown, but the second ball is found to be a Red ball, what is the probability that the first ball is Red? c. Suppose that if the second ball drawn is White, it is replaced with 1 extra White ball and if Red, it is replaced with 2 extra Red balls. A third ball is then drawn at random. What is the probability that it is Red? 3. Three machines A, B and C produce respectively 50%, 30% and 20% of the factory output. The percentages of defective output of these machines are 3%, 4%, and 5%. a. If an item is selected at random, find the probability that the item is defective. 4. A fair coin is tossed 8 times. Call Head a success. a. What is the probability of exactly 2 Heads? b. What is the probability of getting at least four Heads? c. What is the probability of no Heads? d. What is the probability of getting at least one Head? Good Luck