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Unformatted text preview: Stat INA. lotro Probability
Midterm l .I. Sanchez
UCLA Department of Statistics MULTIPLE CHOICE QUESHONE. ONLY ONE ANSWER ISCDRRECT. CHOICE MUST BE NHRKED
UN THE SCANTRDH, AND ALSD HERE ON THE. EXAM. ONLY THE SEANTRDN 1liliilLL BE GRADED.
NO WHILE UN SCﬁNTRDN OR MORE THAN ONE MARK WILL RESULT IN 1} PUINTS FOR THE
QUESTION HGT MARKED, EVEN IF IT IS MRKEII ON THE Exam. You may use the space near the
question for scratch work. but scratch work will not be read. Question 1. A manufacturing company has two retail outlets. It is known that 30% of all potential customers buy
products from outlet l alone. 50% buy from outlet 2 alone. 10% buy from both I and 2. and lﬂﬁ: buy from neither.
Let A denote the event that a potential customer. randomly chosen. buys from outlet I. and let H denote the event
that the customer buys from outlet 1. Which of the following statements is true‘?I ,_ t. eieo=o3 \ X
[b)Pi{t4I"iH}‘=ﬂ 3" '5“)
erasuet=ot i
:ﬁwss of} = as {ﬁt3f ta Pia u or = as Qﬂﬁﬁﬂﬂ 2. Setten applicants have applied for two jobs. How many ways can the jobs be ﬁlled if there are no
djlferences between Ihejobs‘? .ﬂth' ' {If a
{is 4: [cl 4? id) 7 [e] 2 Question 3. Police rcport that TEE: of drivers stopped on suspicion of drunk driving are given a breath test. 35% a
blood test. and see both tests. What is the probability that a randomly selected D‘t‘v'I [Driving 1t‘r’hjle Intoxicated}
suspect is given none of the tests? {a} ll? . x: ml 3M n
(to ﬁloI": "i l: _i l ' c4
{cl {Hid ‘ t..____ __.»'/ to not tel 1184 Question IL An insurance company believes that people can be divided into two classes: moss who are accident
praise {A} and times Who are not {B}. Theirstatistics show that if aperson is aecidentlprone she will have an seeident
[Cl at some time within a ﬁtted lyear period with probability {14. whereas if a person is nonaecident prone this
probability decreases to I12. We know that 3!} percent of the population is accident prone. The joint probability that
a randomly chosen custonter is not accident prone and has an accident within 1 year is: . _ {a} e. 14' ““2.
ts} chaise
(c) not
{a} u. 11
(c) ELSE Queetlon 5. A manufacturing company has three outoftown plants, A. B. and C. The plants are located in different
cities. From among ten employees. three are to be selected to go to plant A. In hemmany ways can this selection be
made? 3' is] 1000 l : ' ‘""
its] at» {He} no to] ass is] EBB Qnmﬂon IS. A customer visiting the suit department of a certain store will purchase a suit with probability {1221
a shirt with probability {13. and a tie with probability {1.23. The customer will purchase both a suit and a shirt
with probability Ill]. both a suit and a tie with probability {114 and both a shirt and a tie with probability 1110.
A customer will purchase all three items with probability tlﬂﬁ. Let A be the event that the customer purchases a
suit. B the event that the customer putshasce a shirt and C the event that the customer psirchascs a tie. What is the
probability that a customer purchases exactly one _ot'_ these items? '1: {a} ”I a" . . r [on its , eat} “it
IE'I'III r._' I Griu : {c} not IE1": a use so; l l  {e} DESK 116$th 'lr'. Ninety percent of all babies survive delivcty. However, 15 percent of all births involve Cesareant C}
sections. and when a C section is perfonned the baby survives 92 percent of the time. if a randomly chosen pregnant
woman does not have a C section. what is the probability that her baby survives? .~ “' '5'" Qli'bise be {a} 13.92
lb] 0159335 es ‘essa‘tx "5 t a. id] 11345
{e} 1 Question 8. 0f the persons arriving at a small airport. mm H}! on major airlines. 30% ﬂy on privately owned
airplanes. and [(1% fly on commercially owned airplanes not belonging to an airline. 0f the persons arriving on
major airlines. see are traveling for business reasons; the smreoporrding ﬁgures are 150% for persons arriving on
private planes and 90% for persons arriving on other commercially owned planes. For a person selected at random
from a group of arrivals in oorrtmereial airliners. ﬁnd tire probability that the person is traveling on business. [a] 0.3153
{lo} 0.?
{c} I113 ...;... _ (a) diff;
[e] are Question 9. Suppose a sampIe spam 5 emaists of 4 outeomes: S = [ a].oz.e3.ml. Which functions deﬁne a
probability function? is] Plan} = inﬁdel n 1.?th = Lima} =i
it} Has = smog} = are.) = simian =§
in} Pics = was = late) = Leas =5
refrim} = was = iﬂasi = Laos = i
e: Pta12r=éﬂszl=i.Pta3}=i.Ptasi=v} Question 10. In I988 the results of the Physicians‘ Health Study Research Group study were reported in the New
England Journal of Medicine. in this study 2207] male physicians (aged from 40 to 84) were randomly assigned to
two groups. One group took an aspirin every second day and the other group took a placebo. a pill with no active
ingredient which looked just like an aspirin. The participants did not know whether they were taking aspirin or the
placebo. After ﬁve years the number of participants in each group who had had a heart attack was recorded. The
results are shown in the table found on this page. For male physicians aged 40 to 84. the risk of having a heart attack for those taking a placebo every second day
is.. (a) twice the risk for those taking aspirin lb]: 0.3 the risk for tltose taking aspiring
to] 0.55 the risk for those taking aspiring.
{d} 3 times the rial: for those taking aspirin
flier1.013 the risk for most: taking aspirin titration 1]. What is the chance that among a grail: of four people chosen at random at least two were hunt in the
same month {not necessarily the same year}. Mark your answer here and in the scantron.  tnfiefsrcs “a. . .__'_ ,;:, .3
~'— "' ' . ] ta ta .1 Eli) sass
lcl 0.21%
{d} on?! '
{e} llml Question 12. A system with E: independent components is such that the system will fail if at least one of the
individual cmnponents fail. The probability that a component fails is 0.02. Let. A be tlte event that the system fails. How many outmmes of the sample space are in at? {all 0.114]
{h} 0.035042
{c} 04 id} 46550
no ss__.'= Question 13. Suppose that you and a friend are matching balanced coins {i.e.. each coin has probability ill at
landing head). Each of you tosses a coin. If the upper faces match and both are both head. you win 5.03 dollar, it“ they do not match. you lose 3.00 dollar [your friend wins 3.00 dollar}. If they match and they are both tail. you win
1 dollar. Let X be the random sample representing your winnings. Your expected gains and standard deviation are. respectively. _—._ _ I:
’ 'g't'i.r""l'r.1.~" 11213.“; {a} F“ 0.5: o“: 0.2 lb} y=01 rr= 3.00 {e} p=3:o'=0.5 '. {a} =0;o'=3.3lﬁt5 {almanac Question 14. A tom: has lDtllJ people. 11m people can be classiﬁed by their income level and their education.
with the following information: I 1112' have 516 years of sohoolittg and make 3 $50. III)
I 30D have 3 it: years of schooling and make 3 $59,012!)
I dill) have 5 16 years of sohooling and make 5 $50. ﬁll). The joint probability that a randome chosen person has :r if: years of schooling and makes a» $5131 Gill] is (a) ill
{bl 113?
{cl 0.5
{at 11:45.
{e} [3.62 Question 15. A doctor is studying the relationship between blood pressure and heartbeat abnormalities in her pa
tients. She tests a random sample other patients and notes their blood pressures (high. low. or neutral} and their
heartbeats [regular or irregular]. She ﬁnds that: e 14% have high blood pressure. I 22% have low blood pressure. I 15% have an irregular heartbeat. I Of those with an irregular heartbeat, onethird hatre high blood pressure. 1: Of those 1with normal blood pressme, oneeighth have an irregular heartbeat. What portion of the patients selected have irregular heartbeat and normal blood pressure? (“34% . _. H L H mm“ l 3' l :2. 3. . '
{at so 1‘1 :11 int !oo
(also Question 16. It is known that 40 percent of the romantic dates that an adult has while single are not much fun.
No college students seeking a romantic partner decide to start going out independently on dates with other people
chosen at random. to look forthe fun date out there. Find the probability that both of them ﬁnd their ﬁrst fun date in
the 5th date. Mark your answer here and in the scantron. {a} 0.601
{b} 0.130255
"threesome
{Hi Ami
{e} HUSH?!
Question 11. Let X denote it random 1iraiiahle that has the following piobahility mass function. ““
IEIIiEIiEI at is the variance of X 'i' [mark yousr answer hct'e_end in the scentmn} mot F' —G.’1s0.i§=tf‘.1
[h] {3.51
I!” “'3
dim
is low '31 'l[FL +U.ir0.11fg_3o.s‘ Quadsu 15. A system with 6 independent components is such that the system fails it‘ at least one of the individual
oomponeuts fail. The probability that a compoth fails is llﬂl. Let A be the event that the system fails. What is the probability that the system fails? (Mark your answer here and in the seantron.)
is} 0.93? {hi 13.3353 r h . L [cl 1 I Edi 0.543 @1111“ Question 19. A system consists of three independent components in parallel. The system works it at least one ot the
cmnpooents works. If each componem works with probability 0.75, what is the probability that the system works? {e} 1
{13} 0.03 {c} p.925
mi mix
to} {125 ﬂotation 1] Supposl then! an: 5'!) Pwplﬂ in a group. 30 of them wow and 20 man. Suppose wo wish to aoquiro a random sample of IE poop]; fmm tho sloop. Lot A both: wont that whore an: 4 women andﬁ men in mcnmplc. Find tho probability of A. } ilﬁ' b ”H . T! I. 'l {a} {uni”1%.. it} £1.89 {o} [11115 {d} 3.34
m 0.6? mmmm m
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 Fall '07
 Wu
 Probability, I. I. I.

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