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- The four brands of soap have the current market share of 0.23, 0.28, 0.25, and 0.24 for brands A, B, C, and D, respectively. Below are the transition probability matrix of the soap brands based on their annual performance and the number of customers using the brands. 0.4 2300 T 0.3 2800 0.2 2500 2400 From/To A B C D A 0.2 0 0.3 0.3 B 0.3 0.2 0.5 0.4 C 0.1 0.5 0 0.3 D 0 a) What is the market share of Brand D in the long run? Answer in 2 decimal places. c) What is the mean return time of Brand A? Answer in 2 decimal places. b) How many customers will shift preference in using Brand C soap in the long run? Number of Customers d) What is the percentage change of Brand B? Answer in percentage and in 2 decimal places.In a group of 80 students, there are 50 girls and 30 boys such that 65% of the girls graduated from private schools and 15% of the boys graduated from private schools. If a student is randomly selected from this group, find the probability that the selected student graduated from a private school (use the shown tree diagram for your solution). Private School girls Public School Private School boys Public School O 0.800 0.406 O 0.538 O 0.463Your company bids for two contracts. You believe the probability that you get contract #1 is 0.7. If you get contract #1, the probability you also get contract #2 will be 0.3, and if you do not get contract #1, the probability that you get contract #2 will be 0.2. Complete parts a through e below. Question content area bottom Part 1 a) Are the outcomes of the two contracts bids independent? Explain. b) Find the probability you get both contracts. c) Find the probability you get neither contracts. d) Let X be the number of contracts you get. Find the probability model for X. x 0 1 2 P(x) e) Find the expected value and standard deviation of X.
- Mrs b. A salesman has a 40% probability of making a sale to any customer who enters his department. On a typical day, he will meet 20 customers. What minimum number of sales will he have an 95% certainty of making for any given day.Consider an M/M/1 queueing system. Find the probability of finding at least n customers in the system.21. A box contains five red, two white, and three green marbles. If a marble is selected at random, find these probabilities. b. That it is green. a. That it is red. d. That it is not green. c. That it is not red.
- Consider a system of four flipped coins. (&) What s the probability that two land heads and the other two tails? (b) Label the four coins 1.2, 3, and 4. Make a chart that lists the various possible configurations that have two heads and two tails. Is the number of configurations on your chartHw 4 The following information relates to the probability of two different managers selecting a salesperson for a job: Probability of Manager Sam choosing a Salesperson is 0.5 Probability of Manager Alex choosing a Salesperson is 0.3 Over the last 10 working days, Manager Sam has worked for 6 days and Manager Alex worked 4 days. Only one manager works in a day. Required: Build a Tree diagram to show the probabilities of a Salesperson being selected. Show the different branches of the Tree diagram with all the calculations. Include in the Tree diagram the overall probabilities.Becky and Carla take an advanced yoga class. Becky can hold 29% of her poses for over a minute, while Carla can hold 35% of her poses for over a minute. Suppose each yoga student is asked to hold 50 poses. Let B the proportion of poses Becky can hold for over a minute and C = the proportion of poses Carla can hold for over a minute. What is the probability that Becky's proportion of poses held for over a minute is greater than Carla's? Find the z-table here. O 0.159 O 0,259 0 0.448 O 0,741 Save and Exit Next Submit Math and rem 96 & 7 8 9. 10
- 1. A class of 18 pupils consist of 11 girls, 4 of whom are left-handed, and 7 boys, only one of whom is left-handed. The two pupils are to be chosen at random from the class to act as monitors. Calculate the probabilities that the chosen pupils will consist ofa. One girl and One boyb. One girl who is left-handed and one boy who is left-handedc. Two left-handed pupilsA system has five components connected as shown in the diagram. Assume A, B, C, D, and E function independently. If the probabilities that A, B, C, D, and E function 0.50, 0.65, 0.75, 0.95, and 0.80 respectively, what is the probability that the system fails?When three athletes compete, the probability of winning the race for the first athlete (A1) is 1/3, the probability for the second athlete (A2) to win the race 1/4, and the probability for the third athlete (A3) to win the race 1/5. Athletes compete 2 times. What is the probability of winning the first race A1 and second race A2, or first race A1 and second race A3?Note: Use the tree diagram. The requested P(A1A2 or A1A3=P(A1A2UA1A3)=P(A1A2)+P(A1A3)
