Mathematics for Business Decisions, Part IHomework 2Solution:Solution:Mathematics for Business Decisions, Part IHomework 2forMath 115a, Section: Instructor: Date: byTeam: We, the undersigned, maintain that each of us participated fully and equally in the completion of this assignment and that the work contained herein is original. Furthermore, we acknowledge that sanctions will be imposed jointly if any part of this work is found to violate the Student Code of Conduct, the Code of Academic Integrity, orthe policies and procedures established for this course. ______________________________ ______________________________Name (printed) Signature______________________________ ______________________________Name (printed) Signature______________________________ ______________________________Name (printed) Signature______________________________ ______________________________Name (printed) Signature______________________________ ______________________________Name (printed) Signature1. Use repeated computation in the file Bank Customers.xls to generate a set of twenty fractions for periods of one business month of 21 days. (ii) What is the largest fraction that you found? (iii) What is the smallest fraction that you found?Solution: 2. A fair die is rolled twice and the number of spots on the upper face is recorded for eachroll. We can take all possible pairs of numbers, each of which is between 1 and 6, as our sample space, S. Since the die is fair, we will assume that each of the 36 outcomes is equally likely, and therefore, that they all have the same probability. Find the probability of each of the following events:E: The first fact is odd.F: The sum of the faces is greater than 8.G: The sum of the faces is even.Solution: 3. An inspector will visit your plant on one of the seven days during the coming week, and is equally likely to arrive on any of the days. Use Sa} F, Th, W,Tu, M, Su,{Sas a sample space for the experiment of observing the day on which you are inspected. (i) Use the probability properties to find the probability of being inspected on any given dayin the sample space. (ii) If E is the event that you are inspected on a weekend day, compute )(EP. Indicate the property that you use in each step of the work.Solution:4. Consider newly incorporated small businesses in a certain area. Data indicates that there is a 69% chance that a business fails within the first year, a 21% chance that a business is its owner’s first venture, and a 19% chance that a business fails during the first year and is its owner’s first venture. What is the probability that a business does not fail in the first year? Solution: )6,6()5,6()4,6()3,6()2,6()1,6()6,5()5,5()4,5()3,5()2,5()1,5()6,4()5,4()4,4()3,4()2,4()1,4()6,3()5,3()4,3()3,3()2,3()1,3()6,2()5,2()4,2()3,2()2,2()1,2()6,1()5,1()4,1()3,1()2,1()1,1(S5. Consider newly incorporated small businesses in a certain area. Data indicates that there is a 69% chance that a business fails within the first year, a 21% chance that a business is its owner’s first venture, and a 19% chance that a business fails during the first year and is its owner’s first venture. What is the probability that the business does not fail during the first year and that it is not its owner’s first venture?Solution: 6. The probability that you get a raise is 0.68, the probability that you get your own officeis 0.41, and the probability that you get a raise and your own office is 0.24. Find the probability that you get your own office but not a raise.Solution: 7. Best Builders has bid on contracts for the construction of two large office buildings. The owner of the company estimates that the probability of being awarded the first contract is 0.4, the probability of being awarded the second contract is 0.6, and the probability of being awarded both contracts is 0.1. What is the owner’s estimate of the probability of being awarded neither of the
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