Review Exercises for Probability in Chapter 1compiled by Veronica Burgdorff and Joe KahligFall 20091. Give the sample sp ace of an experiment that consists ofdrawing a card from a standard deck and recording itssuit.2. Toss a red die and draw a ball from a box containing 3green and 5 yellow.(a) List the event A ={a green ball is drawn}.(b) List the event B ={a three is rolled}.(c) List the outcomes in A ∩ B.(d) Are A and B mutually exclusive?3. Jim has a drawer containing eight blue, fi ve black, and sixwhite socks. If he pulls out two socks at random, whatis the probability that Jim will draw a matching pair ofsocks?4. A box contains four red, five white, and eight yellow mar-bles. A marble is drawn.(a) What is the probability that the marble is red?(b) Assuming that t he first marble is red and is notreplaced, what is the probability that the secondmarble drawn is red?(c) Assuming that the first marble is not rep laced,what is the probability that a red marble is notdrawn in neither the first nor second draw?5. The weather forecaster at station W IBV is correct 82%of the time; the forecaster at neighboring station WI LA,65% of the time. What is the probability that on a givenoccasion, one of the two (or both) will be correct?6. If Nancy selects a security from a list of three growthstocks, seven income stocks, and fi ve bonds, what is t heprobability that she will select a bond or a growth stock?7. A manufacturer of automobiles receives 1000 car radiosfrom each of th ree different supp liers. Unknown to themanufacturer, there are five defective radios from supplierA, seven from supplier B, and only two from supplier C.As a means of qu ality control, one radio is selected at ran-dom from each of the shipments. What is the probabilitythat(a) All the radios selected are in working order?(b) At least one of the selected radios is defective?8. A computer from the Electronic Computer company con-sists of a keyboard, a monitor, a CPU, and a printer. Thesuppliers for these four units claim to have a percentage-of-defects record of 2.5%, 1%, 4%, and 6%, respectively.What claim of reliability can the Electronic Computercompany make, in terms of the percentage of its compo-nenants that are probably defective?9. A retailer receives two shipments of TV sets. The firstshipment, from company A, is known historically to be5% defective. The second, from company B, is knownto be 3% defective. If one item is selected from eachshipment,(a) What is the probability of selecting one good TVand one defective TV?(b) What is the probability of selecting two good TVs?10. Box A contains three red marbles and two white marbles;box B contains four red marbles and six white marbles;and box C contains three red marbles and seven whitemarbles. If a box is selected at random and a marble isdrawn from this box, what is the probability the marbleis red?11. A new test for Alzheimer’s Disease will detect the disease95% of the time in a person who has Alzheimer’s. Inaddition, the test will falsely detect the disease 15% of thetime in a healthy person. If the t est is give to a personselected at random from a group of people, 90 of whomare healthy and 10 of whom have Alzheimer’s, what is theprobability that(a) Alzheimer’s will be detected if the p erson has thedisease?(b) Alzheimer’s will be falsely detected if the persondoes not have the disease?(c) the person has Alzheimer’s if the test detects thedisease?12. A chef’s school is 60% male and 40% female. Seventypercent of the males and 90% of the females like eatingcrab legs for dinner. A student from the school is selectedat random.What is the probability that a member of this chef’sschool(a) What is the probability that the stud ent is male orlikes eating crab legs for dinner?(b) If the student likes eating crab legs for dinner, whatis the probability that the student is female?(c) What percentage of the students like eating crablegs for dinner?13. At t.u., 35% of the freshmen failed math, 20% failed En-glish, and 10% failed both math and English.(a) What is the probability that a freshman failed ex-actly one of the courses?(b) If a freshman fail Math, what is the probability thatthey failed En glish?14. Two marbles are selected in succession, without replace-ment, from a box containing five blue and three greenmarbles. What is the probability that the second marbleis blue, given that the first marble was green?15. Sixty percent of the toasters in a warehouse come fromthe Hot-Slice Co., and of those toasters, 3% are defective;40% come from the Warm Morning Co., and of those 5%are defective. What percentage of the toasters in thewarehouse are defective?Solutions.1. S ={hearts, diamonds, spades, clubs}2. (a) A ={(1,g), (2,g), (3,g), (4,g), (5,g), (6,g) }(b) B ={(3,g), (3,y)}(c) A ∩ B ={(3,g)}(d) no3. 0.30994. (a)417= 0.2353(b)316= 0.1875(c)1317∗1216= 0.57355. 0.9376. 0.53337. (a)9951000∗9931000∗9981000= 0.9861(b) 1 − 0.9861 = 0.01398. P( n on-defective system) = 0.975 ∗ 0.99 ∗ 0.96 ∗ 0.94 =0.8710or 87.1% of the systems are not defective. Hence 12.9%of the systems are defective.9. (a) 0.05 ∗ 0.97 + 0.95 ∗ 0.03 = 0.077(b) 0.97 ∗ 0.95 = 0.921510.133011. (a) 0.95(b) 0.15(c)0.1∗0.950.1∗0.95+0.9∗0.15= 0.413012. (a) 0.96(b)613= 0.4615(c) 78%13. (a) 0.35(b)1035= 0.285714.5715.
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