WIR Math 141-copyright Joe Kahlig, 11B Page 1Sample Problems For Exam 3Compiled by Joe KahligThis collection of questions is intended to give you an idea of different types of question that might be asked onthe exam. There may be questions on the exam that are not found on this handout.These questions cover Chapter 7 and section 8.1-8.4 in the Applied Finite Mathematics, 10thedition by S. T. Tan.Video solutions can be found at this link:http://www.math.tamu.edu/ ∼kahlig/141WIRpage.html1. Explain the difference between mutually exclusive and independent.2. Roll a 10 s ided die and an 8 sided die. What is the probability that(a) A sum of 3 or a sum of 6 is rolled?(b) A sum of 6 or one of the die(at least one die) has a 2 on it.(c) A sum of 8 is rolled if the ten sided die has an even number on it.(d) A sum of 12 is rolled provided a six is cast (at least one six is rolled).(e) A sum of 8 and a 6 is rolled on one of the die.3. Jim has a drawer containing eight blue, five black, and six white socks. If he pulls out two socks at random,what is th e probab ility that Jim will draw a matching pair of socks?4. A box contains four red , five white, and eight yellow marbles. Two marbles are drawn without replacement.(a) What is the probab ility that the first marble is red?(b) Assuming that the first marble is red , what is the p robability that the second marble drawn is red?(c) What is the prob ab ility that a red marble is not drawn in neither the first nor second draw?5. A student takes a 10 question multiple choice exam in which each question has 4 answers. Being unpreparedfor the exam, the student rand omly guesses at each of the question.(a) What is the probab ility of getting exactly 6 of the questions correct?(b) What is the probab ility of passing the exam? (Grades below 70 don’t pass.)(c) What is the prob ab ility that the student get the fi rst three correct and the last 7 wr on g?(d) How many q uestions should the student expect to get correct?6. The weather f orecaster at station WIBV is correct 82% of the time; the forecaster at neighboring stationWILA, 65% of the time. If the forecasters make their weather predictions independently of each other, whatis the p robability that on a given occasion, one of the two (or both) will be correct?7. A manufacturer of automobiles receives 500 car radios from each of three different suppliers. Unknown tothe manufacturer, there are five defective radios from supplier A, seven from supplier B, and only two fromsupplier C. As a means of quality control, one radio is selected at r an dom from each of the ship ments. Whatis the p robability that(a) All the radios selected are in working order?(b) At least one of the selected radios is defective?(c) exactly one of the selected radios is defective?WIR Math 141-copyright Joe Kahlig, 11B Page 28. A new test f or Alzheimer’s Disease will detect the disease 95% of the time in a person who has Alzheimer’sand will fail to detect it 5% of the time. In addition, the test will give a false positive 15% of the time. Ifthe test is give to a person selected at r an dom from a group of subjects, 90 of whom are healthy and 10 ofwhom have Alzheimer’s, what is the probability that(a) Alzheimer’s will not be detected if the pers on has the d is ease?(b) the person has Alzheimer’s if the test detects the disease?(c) If the person takes the test twice, what is the probability that the person has the disease if both testare positive.9. A chef’s school is 60% male. Seventy percent of the males and 90% of the females like eating crab legs fordinner. A student of the school is selected at random.(a) What is the probab ility that the student is male or likes eating crab legs for dinner?(b) If the student likes eating crab legs for dinner, what is the probability that the student is female?(c) What percentage of the students like eating crab legs for dinner?10. Let E and F be two events and P (E) = .35,P (F ) = .55, and P (E ∩ FC) = .15. Answer the following questions.(a) P (E ∩ F ) =(b) C ompute the probability of exactly one of th ese events occurring.(c) Ar e E and F mutually exclusive?(d) Are E and F independent?(e) P (F |E) =(f) P (E ∪ F ) =(g) P (EC|F ) =11. Classify the following random variables as finite discrete, infinite discrete, or continuous.(a) X = The number of times a die is cast until a 5 is rolled.(b) X = How long it takes you use an ATM machine.(c) X = The numb er of cadets in a class of 100 students.(d) X = The temperature of the human body.12. Fifteen people are selected at random. What is the probability that at least 2 of the people in this group(a) were born on the same day?(b) were born in the same month? Assume that months are equally likely.WIR Math 141-copyright Joe Kahlig, 11B Page 313. The accompanying data were obtained in a study conducted by th e manage of the Sav-More Supermarket.In this s tudy the number of cus tomers waiting in line at the exp ress checkout at the beginning of each3-minute interval between 9 a.m. and 12 noon on Saturday was observed.Numberof Cu stomers 0 1 2 3 4 5 6 7 8 9 10Frequency 1 4 2 7 14 8 10 6 3 4 1(a) Find the probability distribution for the random variable X, where X denotes th e number of customersobserved waiting in line.(b) Draw a prob ab ility histogram. Be sure to label the pictur e.(c) P (2 ≤ X ≤ 6) =(d) P (X ≤ 8) =(e) Find the number of people th at we would expect to be in line at any given time on S aturday.(f) Compute the mean, median, mode, variance, and standard deviation for the f requency chart. Be sureto label the answers.14. Find the odds of drawing an ace, from a standard deck of cards, on the second draw if we k now that thefirst card drawn was a king and cards are not replaced after they are drawn.15. The odds against an event E occurrin g are 3 to 19. What is the probability of E occurring?16. Fred wants to purchase a 10-year term life insurance policy that will pay the beneficiary $100,000 in the eventthat Fred doesn’t surv ive the next ten years. Using life insurance tables, he determines that the probabilitythat he will live another ten years is .97. Wh at is the minimum amount that he can expect to p ay for hispremium?17. Suppose you roll two fair six sided dice and sum the numbers that sh ow. You win twice what you paid if a7 or 11 shows up. You lose wh at you paid if a 2,3, or 12 shows up. For anything else that shows …
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