Question

Do the following problems. 1. Each of three barrels from a manufacturing line are classified as either above (a) or below (b) the target weight. Provide the ordered sample space. 2. The heat on each of two soldered parts is measured and labeled as either low (l), medium (m), or high (h). State the number of elements in the ordered sample space. 3. Consider the set of Beatles songs with a primary writer as either Paul McCartney (P) or John Lennon (J). From this set, ten songs were randomly chosen and classified by their main composer (i.e. primary writer). State the number of elements in the ordered sample space. NOTE: both artists composed many songs, way more than 10. 4. The following two questions appear on an employee survey questionnaire. Each answer is chosen from the five-point scale of 1 (never), 2, 3, 4, 5 (very often). i.) How often do you interact with the marketing team? ii.) How often do you interact with the accounting team? State the ordered sample space. HINT: Consider each person’s response to be a two-digit number. You MUST state the total number of elements in this sample space for full credit. 5. The concentration of chlorine in the air is measured in parts per billion (PPB) and recorded to the nearest PPB. State the sample space. 6. This experiment involves repeatedly calling a busy phone line until a connection is made. Provide the sample space. 7. Use a Venn diagram to verify that (A ∩ B) 0 = A0 ∪ B0 8. Suppose you want to make a sandwich and you can choose either white, rye, or wheat bread, and you can choose either ham or turkey and you can choose either cheese or no-choose. Describe the set of all possible sandwiches using a tree diagram. 9. A set of 8 operations can be done in any order. How many unique orderings are there? {more on next page...} 1 10. A manufacturing process consists of 8 operations, however, the 3 machining operations must be completed before the remaining 5 assembly operations can begin. The 3 machining operations can be done in any order, as can the 5 assembly operations. How many different production sequences are possible? 11. Three attempts are made to read data in a magnetic storage device before an error recovery procedure is used. If there are three failures, then there is a subsequent error recovery procedure that attempts up to two repositionings before an “abort” message is sent. Let s denote the success of a read operation f denote the failure of a read operation S denote the success of an error recovery procedure F denote the failure of an error recovery procedure A denote an abort message sent. State the sample space of this experiment. 12. Samples of emissions for three suppliers are classified for conformance to air-quality specifications. The results from 100 samples is summarized as follows: Conforms Yes No 1 20 8 Supplier 2 27 10 3 30 5 Let A be the event that a sample is from supplier 1 and B be the event that a sample conforms to specifications. Determine the number of samples in A0 ∩ B, B0 , A ∪ B. 13. In a sheet metal operation, 5 notches and 4 bends are required. The notches are indistinguishable from each other, as are the bends. If the operations can be done in any order, how many distinct ways of completing the manufacturing are possible? 14. In a chemical plant, 24 holding tanks are used for final product storage. Four tanks are selected at random without replacement. Suppose that six of the tanks contain material in which the viscosity exceeds the customer requirements. What is the probability that exactly one tank in the sample contains high-viscosity material? 15. Consider picking a number at random from the set of counting numbers from 1 to 25. (a) Describe the sample space S. (b) Let T denote the event that the number drawn is divisible by 3. Describe T. (c) Let B denote the event that the number drawn is a prime number. Describe B. (d) Describe the event B0 (e) Describe the event T ∩ B {more on next page...} 2 16. Consider an experiment where two 6-sided dice are rolled. We can describe the ordered sample space as below where the first coordinate of the ordered pair represents the first die and the second coordinate represents the second die. (a) Describe the event E that the sum of the two dice is 5. (b) Describe the event F that the number of the first die is exactly 1 more than the number on the second die. (c) If the dice are ‘fair’, are all 36 of these possible outcomes equally likely? 17. Your garage door has an outdoor key-pad (with the numbers 0 to 9 on it) that uses a 4-digit code. Suppose a thief approaches your garage and notices that four particular numbers are very well-used. If we assume the code uses all four numbers exactly once, what is the maximum number of 4-digit codes the thief has to try? 18. Suppose a coin is tossed, then a 6-sided die is rolled, then a card is chosen from a 52- card deck. Use the multiplication rule for counting to determine how many elements are in the sample space.

Answer 1