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- Again consider a Little League team that has 15 playerson its roster.a. How many ways are there to select 9 players for thestarting lineup?b. How many ways are there to select 9 players for thestarting lineup and a batting order for the 9 starters?c. Suppose 5 of the 15 players are left-handed. Howmany ways are there to select 3 left-handed outfieldersand have all 6 other positions occupied by right-handedplayers?Suppose that an experimenter tossed three balanced coins. He defined X1, to denote thenumber of heads and X2, is to denote the amount of money won on a daily lotto bet in SouthAfrica in the following manner. If the first head occurs on the first toss, R1 (one rand) is won. Ifthe first head occurs on toss 2 or on toss 3, R2 or R3 is won respectively. If no heads appear,the R1 (that is, win −R1) is lost.Findi) the joint probability function of X1and X2. ii) the probability that less than 3 heads will occur and the student will win R1 or lessSuppose that an experimenter tossed three balanced coins. He defined X1, to denote thenumber of heads and X2, is to denote the amount of money won on a daily lotto bet in SouthAfrica in the following manner. If the first head occurs on the first toss, R1 (one rand) is won. Ifthe first head occurs on toss 2 or on toss 3, R2 or R3 is won respectively. If no heads appear,1the R1 (that is, win -R1) is lost.Findi) the joint probability function of X,and X2-) the probability that less than 3 heads will occur and the student will win R1 or less.
- At a company, the quality assuran_ce staff has set up a criter_ion to assure if the quality of their products are ready to be expor_ted. Each of the exported box contains 25 pieces of their product. Three inspection staffs are assigned to do one by one inspection. Namely, the first inspector will randomly select one piece from the box and record if it is defective or non-defective and return that piece to box. The second inspector has repeated the same way of inspection as the first inspector and, lastly, the third inspector also repeats the same action one more time. The criteri_on is as follows. If all inspectors have not found any defective product, then {th_e} box is accepted to be exported. On the other hand, if at least one of the inspector has found the defective product, the whole box must be rejected and must be returned for reproduction. By considering this way of inspection process, find The prob that a box contaning exact_ly 3 defective product would pass the inspection…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.A total of 60 students have taken the discrete math exam which provided 3 questions A, B, and C. There are 34 students who did question A correctly, 20 students did question B correctly, and 45 students did question C correctly. Further, 10 students did questions A and B correctly, 15 students did questions A and C correctly, and 20 students did questions B and C correctly. If all students did at least one question A, B, or C correctly, the number of students did all three questions correctly is….
- consider there is a bag of marbles 23 are red,2 blue marbles,14 purple marbles and 14 green marbles. one marble is chosen at random from the bag. what is the probaility of getting a red marble or a blue marblea 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 rwquiredSuppose there are 10 students participating in a workshop that meets every day of a five-day work week. Each student must present a poster in exactly one of the days of the workshop, and every day of the workshop should have at least one poster presentation. If nk denotes the number of posters presented in day k of the workshop, what is the number of possible quintuples (n1,n2,n3,n4,n5)? I ll rate accordingly.
- In 1975, the automobile industry determined t hat 40% of American carowners drove large cars, 20% drove intermediate-sized cars, and 40% drove small cars. A second survey in 1985 showed that 70% of the large-car owners in 1975 still owned large cars in 19 5, but 30% had changed to an intermediate-sized car. Of those who owned intermediate-sizedcars in 1975, 10% had switched to large cars, 70% cont inued to driveintermediate-sized cars, and 20% had changed to small cars in 19 5.Finally, of the small-car owners in 1975, 10% owned intermediate-sizedcars and 90% owned small cars in 19 5. Assuming that these trendscontinue, determine the percentages of Americans who own cars of eachsize in 1995 and the corresponding eventual percentages.Assume that you have 6 red balls and 10 blue balls from which randomly to select two without replacementA television director has to schedule commercials during 6 time slots allocated to commercialsduring the national telecast of the first period of a Montréal Canadiens hockey game.(a) In how many ordered ways can the television director schedule 6 different commercialsduring the 6 time slots?(b) In how many ways can the television director fill the 6 time slots allocated tocommercials, if there are 4 different commercials, of which a given one is to be shown 3times while each of the others is to be shown once?(c) As in (b) except the commercial shown three times can’t be shown before or after itself(i.e., not consecutively). How many ways can the television director fill the 6 time slots?