STAT 210 Problems Probability, Fall 2014

MultipleChoice Questions Pr obability - General 1. The probability that the Red River will flo od in any given year has b een es timated from 200 years of h istorical data to b e one in four.This me an s: (a) The Red River will flo od every four year. (b) In the next 100 years, the Red River will flo od exactly 25 times. (c) In th e last 100 years, the Red River flo o ded exactly 25 times. (d) In the next 100 years, the Red River will flo od ab out 25 times. (e) In the next 100 years, it is very likely that the Red River w ill flo od exactly 25 times. 2. The chances that you will ticketed for illegal parking on campus are ab out 1/3. Durin g th e last nine days, you have illegally parked every day and have NOT b een ticketed (you lucky p ers on)!To day, on the10 th day, you again decide to park ille gally. Th e chances that you will b e caught are: (a) gre ate r th an1/3 b ec ause you were not c au ght in th e last nine days. (b) less than 1/3 b ecause you were not caught in the last nine days. (c) still equalto 1/3 b ecause the last nin e days do not affect th e proba- bility. (d) equal to 1/10 b ec ause you were not cau ght in th e last nine days. (e) equal to 9/10 b ec ause you were not cau ght in th e last nine days. 3. The ch an ce th at a p e rson will contract AIDS after a sexual contact with an infected partner has b een es timated to b e 1/4.This means: 1 (a) A p erson will b e infe cted after exactly 4 sexual contac ts with inf ected partners. (b) Of 1000 p eople having sexual contacts with infe cted partners, exactly 250 will b e come in fec te d. (c) Of 200 p eople havin g sexualcontacts with infe cted partners, ab out 50 will b e come in fe cted. (d) In exac tly 25% of all sexual contacts with infec ted p artners, the in- fe ction will spread. (e) Of 20 p e op le having se xual contacts with in fected partners, it is very likely that exactly 5 p eople will b e come in fec te d. 4. A ran dom variableY has the following distribution: Y | -1 0 1 2 P(Y)| 3C 2C 0.4 0.1 The value of the cons tant C is: (a) 0.10 (b) 0.15 (c) 0.20 (d) 0.25 (e) 0.75 5. A ran dom variableX has a probability d is tribution as follows: r | 0 1 2 3 P(R=r) | 2k 3k 13k 2k Then the probability th at P r(X < 2.0) is e qu al to (a) .90 (b) .25 (c) .65 (d) .15 c 20 06 Carl Ja mes Schwa rz 2 (e) 1.00 6. Supp ose that the allele for tallness (T) is dominant over shortness (t); that for Yellow (Y) is dominant over green (y); and that for rou nd nes s (W) is dominant over wrin kled(w). Supp ose we cross two plants with genotyp es TTYyWw an d TtYyWw. Th e probability of a Tall, Yellow, Rou nd plant is: (a) 9/16 (b) 3/32 (c) 1/16 (d) 9/32 (e) 3/16 7. It has b een estimated that ab out 20% of p eople b etween th e ages of18 and 25 have used marij uan a in the las t year. Wh ich of the followin g is CORRE CTab out this statement? (a) Five p eople of this age group were rand omly selec ted.This means that exactly one of them mus t have use d marij uan a in the las t year. (b) Twenty p eople were randomly se le cted from th is age group. Eighteen of them use marij uan a in th e last year.The ne xt p erson selec te d at random will have a lower probability of us in g marij uana. (c) Ten p eople were randomly se le cted from th is age group. Non e of them have us ed marijuan a in the last ye ar.The ne xt p erson selected mu st have a highe r probability of using marijuana in th e last year. (d) A th ou sand p eople from th is age group were randomly selected. It is not unu sual to fin d that 217 of them have used marij uana in the last year. (e) A million p eople from this age grou p we re randomly selec te d. Th ere must b e exactly 200,000 of them that have use d mariju ana in the last year. c 20 06 Carl Ja mes Schwa rz 3 The following two questi ons r efer to the follow ing situati on. All human blo od can be “ABO” typ ed as b elonging to one of A, B, O, or AB typ es. Th e actu al distribution varie s s lightly among different grou ps of p eop le,b ut f or a randomly chose n p erson from North America, the following are the approxim ate probabilities: Blood type O A B AB Probability .45 .40 .11 .04 8. Consider an accident victim with typ e B blo o d. She can on ly receivea transfusion from a p erson with typ e B or typ e O blo o d. What is the probability that a rand omly chos en p erson will b e s uitable donor? (a) ab out .11 (b) ab out .04 (c) ab out .15 (d) ab out .45 (e) ab out .56 9. Wh at is th e p robab ility that b oth p eople in a couple will have the SAME blo od typ e if matings are random with resp ect to blo od typ e, i.e. one partner’s blo od typ e do es not influence the blo od typ e of the other partner. (a) ab out .21 (b) ab out .16 (c) ab out .002 (d) ab out .01 (e) ab out .38 c 20 06 Carl Ja mes Schwa rz 4