” 辅导MA 581编程、 写作C/C++程序Salins MA 581 Midterm Exam Feb 27, 2019Instructions: Write all of your answers in the blue book. Explain all of your steps. There is no need to simplify Arithmetic (unless stated otherwise). Leavefactorials, combinations, and sums in your answer. You may not use notes, books, calculators, phones, or the internet. Do not cheat. Some summation formulas are on the back page.1. (20 points)Answer the following combinatorial probability questions.(a) A bucket contains 35 red balls, 45 blue balls, and 10 orange balls.You select 10 balls out of the bucket at random without replacement.What is the probability of Selecting exactly 5 red balls, 4blue balls, and 1 orange ball? Explain all of your steps and do notsimplify your arithmetic.(b) Roll 6 fair dice. A fair die has a 16probability of landing on each ofthe possible six outcomes 1,2,3,4,5, and 6. Each die is independentof all of the others. What is the probability that none of the dicematch each other? Explain all of your steps and do not simplifyyour arithmetic.Salins MA 581 Midterm Exam Feb 27, 20192. (30 points) A hiring director at a company has found that only 5% ofpeople who see a particular job listing are qualified for the advertisedposition. Additionally, she found that 70% of the qualified people whosee the job listing choose to apply for the position while 1% of the unqualifiedpeople who see the job listing choose to apply for the position.Let A be the event that a person who saw the job listing applies forthe job. Let Q be the event that a person who sees the job listing isqualified for the job.(a) Write each of these sentences in terms of A, Q, probabilities, conditionalprobabilities, equal signs, and/or numbers (Your answerto each part should look something like P(A|Q) = .7). You donot need to show work or explain your answers for this part.i. 5% of people who see a particular job listing are qualified forthe advertised position.ii. 70% of the qualified people who see the job listing choose toapply for the position.iii. 1% of the unqualified people who see the job listing chooseto apply for the position.(b) Given that a person who saw the job listing applied for the position,what is the probability that this person is qualified?Explain all of your steps and write your work in a clear and organizedmanner. There is no need to simplify your arithmetic.Salins MA 581 Midterm Exam Feb 27, 20193. (30 points) You roll a fair Die 10 times. A fair die means that theprobability of each outcome 1,2,3,4,5, or 6 is 16. Each roll of the dieis independent of all of the other rolls. Let X be a random variablethat represents the number of times the die lands on 2 during these tenrolls.(a) What are the possible values of X? Explain your answer.(b) Write down the Pmf for X. Explain your answer.(c) Calculate P(X 4). Show all of your work. There is no need tosimplify arithmetic.(d) Calculate the probability that X is an even number. Show all ofyour work. There is no need to simplify arithmetic.4. (20 points) A random variable X has the pmf0 otherwisewhere C is some constant that you need to solve for.(a) Find the value of C that Makes pX a valid pmf. Show that yourchoice satisfies all of the requirements of a pmf. For this problemyou should actually simplify your arithmetic.(b) Calculate P(X 4). Show your work. Simplify your arithmetic.(c) Calculate P(X 2|X 4). Show your work. There is no need tosimplify your arithmetic.Salins MA 581 Midterm Exam Feb 27, 2019Summation formulas Binomial Theorem. Exponential Taylor series. Sine Taylor Series如有需要，请加QQ：99515681 或WX：codehelp
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