A ={ 1, 2, 3, 4, 5, 7)} B = { 1, 5, 6, 8} 22. Concatenation of string {(x,x) & A} 23. Concatenation of string {(x, y) & AB} 24. String concatenation {(x, y) & BA}
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- Construct a Venn Diagram for the scenario. Suppose that a total of 208 students are enrolled in a Math course which offers three classes under Instructor X, Instructor Y, and Instructor Z. 4 students are enrolled under all three instructors. 48 students are enrolled under Instructor. Y. Twice as many students are enrolled under Instructor Y and Z (but not Instructor X) as those who are enrolled under both Instructor Y and X (but not Instructor Z), and 4 times as many as those enrolled under all three instructors. 124 students are enrolled in Instructor Z. 27 students are not enrolled in any class. Students enrolled under both Instructor Y and Z (but not Instructor X) is exactly the same size as the students enrolled under both Instructor X and Z.1. Hugo and Viviana work in an office with eight other coworkers. Out of these 10 workers, theirboss needs to choose a group of four to work together on a project. Suppose Hugo and Viviana absolutelyrefuse, under any circumstances, to work together. Under this restriction, how many different workinggroups of four can be formed?Exercise 3: In a garden center: 25% of the plants are less than a year old, 60% are 1 to 2 years old, 25% have yellow flowers, 60% have pink flowers, 15% have yellow flowers and less than a year old , 3% are more than 2 years old and have neither yellow nor pink flowers. 15% of those who are 1 to 2 years old have yellow flowers, 15% of those 1-2 years old have neither yellow nor pink flowers. It is assumed that the flowers cannot be both yellow and pink at the same time. We choose a plant at random in this garden center. What is the probability that it is less than a year old and has pink flowers? What is the probability that she has pink flowers, given that she is over 2 years old? What is the probability that it is over two years old and has yellow flowers?
- Within a group of 12 women, there are five who have known each other for a long time and have an excellent relationship. The other 7 women do not know the 5 friends nor do they know each other. Whenever a subset of the five friends is equal to or greater than 50% of the number of people in another work group (for example, if there are two of the five friends in the work group of three or four people), then the group work becomes high performance It is desired to form a working group by selecting five women from the 12 women. What is the probability that the work group is high performing? Please indicate your answer in the space provided below as a number between zero and one, to four decimal places.Suppose a man's occupation can be classified as professional, skilled worker, or unskilled worker. Suppose eighty percent of the sons of professional men are professionals, ten percent skilled workers, and ten percent unskilled workers. further suppose that sixty percent of the sons of skilled workers are skilled workers, twenty percent professional, and twenty percent unskilled. finally, in the case of unskilled workers, fifty percent of the sons are unskilled workers and twenty-five percent are in the other two categories. Assume each man has at least one son, and construct a Markov chain by tracing the occupation of a randomly selected son of a particular family over several generations. Construct the transition probabilities matrix. Find the probability that the randomly selected grandchild of an unskilled worker is a professional worker.2.1. Find the least number of cables required to connect 100 computers to20 printers to guarantee that every subset of 20 computers candirectly access 20 different printers. Justify your answer.2.2. The English alphabet contains 21 consonants and five vowels. Howmany strings of six lowercase letters of the English alphabet contain2.2.1. Exactly one vowel?2.2.2. Exactly two vowels?2.2.3. At least one vowel?2.2.4. At least two vowels?2.3. What are the values of these sums?
- a 50 letter combiantion comes from {P,Q,R,S,T,U} where letters can be repeated how many 50 letter combinations can take place while meeting the three conditions conditon 1 - at elast 8 Ps , atleast 8 Qs , and 8Rs conditon 2 - at least 3Us are required conditon 3 - exaclty 5Ss and exaclty 5 Ts are rwquiredShow that in a group of five people (where any two people are either friendsor enemies), there are not necessarily three mutual friends or three mutualenemies.From a box containing 4 defective and 5 non-defective items, how manysamples of size 3 are possible.a. With no restrictionsb. With 1 defective and 2 non-defective itemsc. With 2 defectives and 1 non-defective item if a certain item must be onthe samples chosen
- 7.-The 11colleges of interest to a high school senior include 4that are expensive (tuition more than $20,000 per year), 4that are far from home (more than 200 miles away), and 2that are both expensive and far from home. a. If the student decides to select a college that s not expensive and within 200 miles of home, how many selections are possible? b. If the student decides to attend a college that is not expensive and within 200 miles from home during his first two years of college, and then will transfer to a college that is not expensive but is far from home, how many selections of two colleges are possible?Suppose a die is cast 10 times. Let X1 be the number of terminations in the set {1, 2}, X2 be the number of terminations in the set {3}, X3 be the number of terminations in the set {4}, and X4 be the number of terminations in the set {5, 6}. (a) Find the joint pmf of X1, X2, X3.(b) Find the joint pmf of X3 and X4.(c) Find the conditional pmf of X2, given that X1 = 2.A man finished a job in 5 days. On the first day, he finished 1/m of the job. On the second day, he finished 1/n of the job left. On the third day, he finished 1/m of the job left, and on the fourth day,1/n of the job left. On the last day,1/4 of the job was left to be done. If m,n belongs to N and n>m, find m and n.