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Exercises For Chapter 4 (Quiz 3)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) If a sample space contains only two equally likely outcomes, what is the probability that they both 1) _

°CC;~.50 tV'-~ f <.&"\\ i',J ~ 0 B) 0.25 / ~ ""', CC -\> ~p .. C) 1.00 D) Cannot be determined from the information given. E) 0

- ....h,¥,\ ~'J) ~;\ ~L 2) Which number could be the probability of an event that is almost impossi~ 2)

A) 0.51 B) 0.10 - 5;1 0.01 D) 0.99 E) 1.01

~ n ~0In a sample of 750 of its online customers, a department store found that 420 were men. Use this 3~ _ information to estimate the probability that a randomly selected online customer is a man. f' l""'!:\"f\) -:: i,~

A) 0.42 B) 0.47 C) 0.56 D) 0.44 E) 0.51 _ '" 2£' ~-

\So

@Which of the following assignments of probabilities to the sample points A, B, and C is valid if A, B, 4) _ and C are the only sample points in the experiment?

1 1 1 ~ P(A) =6' P(B) = 3' P(C) = '2

2 2 3 B) P(A) = 6' P(B) = 6' P(C) = '6

1 4C) P(A) :::: 0, P(B) = 6' P(C) = 6

111 D) P(A) :::: 10'P(B) :::: 10' P(C) =10

113 E) P(A) :::: - 4' P(B) = 2' P(C) = '4

1 1 1 r» \ ~ c8-- ~1"0'b, @:;iventhatP(AOrB)::::4,P(A)=6,andP(AandB)==7,find P(B). ':-".e."~-rdv \ ('"oCB\ (f\(\5~ '"1+-__

PU\v \~') :; ,,~f\) ~l-\1\ 1

A) 47 B)~ C).E- D) 23 84 - 84 168 84

L _ L --\ ~'-'~\ (\::0 '-\- b

@P(A) :::: 0.29 and P(B) = 0.17.lf A and B are mutually exclusive, P(A IB) =? 6) _

A) 0.00 B) 0.46 -~C) 0.12 ~ (l\rr~O D) 0.29

- "". E- - yO~») 7) If event A and event B cannot occur at the same time, then events A and B are said to be 7)

A) equally likely. B) independent. C) mutually exclusive. D) None of the above.

1

(9The distribution of Master's degrees conferred by a university is listed in the table. 8) _

\

Major Frequency Mathematics 216 English 207 Engineering 86 Business 176

---p Education 243 ~ ~ ~<l\2.'%

What is the probability that a randomly selected student graduating with a Master's degree has a

major of Ed~n? A) 0.355 B) 0.262 C) 0.004 0)0.738

9) _@suppose A and B are events where P(A) =0.4, P(B) =0.5, arid P(A and B) = 0.1. Then P(A or B) = A) 0.8 B) 0.9 C) 0 0) 0.7

-=iat, > '-\ ~.~ S - . \ 10) _10) Suppose A and B are mutually exclusive events where P(A) = 0.4 and P(B) =0.5.Then P(A and B) =

B) 0.8 C) 0.9 0) 0.7

@The probability that Yehia will pass his math test is~. Find the prob~bility that he will~his 11) _

~~O_ A) 0.04 B) 0.96 C)0.48 0)1.04 ~\,~..-wzv'\i-~ - p(A') -:. ,- f (. A)

@If .A and B are independent events, with peA) = ~ I PCB) = ~, find peA u B). 12) _

3 3 13 0).2..A)s' B) 25' .9 25'

P U~U ,3) -- 's ~ ~ -l ~ *}) 10

13) You randomly select someone from a group of 12.Two of those in the group were born in Kuwait. 13) _

What is the chance you will pick a person born in Kuwait? . ~ A) 1/12=.083 B) 24 C) .167 \ 2 0) 6

_

A) Events A and B have no sample points in common. B) Events A and B are dependent. C) Events A and B are disjoint D) Events A and B are mutually exclusive. E) none of the above

14) If p(A I B) = 0 and P(A) ;t 0, then which statement is false? 14)

....

t15}A business venture can result in the following outcomes (with their corresponding chance of 15) _ \!::JJoccurring in parentheses): Highly Successful (?),Successful (25%), Break Even (25%), Disappointing

(200/0)' and Highly Disappointing (20%). If these are the only outcomes possible for the business venture, what is the chance that the business venture will be considered Highly Successful? ~10% B)5% C) 15% 0) 25% E) 20%

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2

16) The random variable x represents the number of cars per household in a town of 1000 households. 16) __ Find the probability of randomly selecting a household that has more than two cars.

Cars Households p l i- '> 2- ') z: P l ~ z: 3> ") --\ ~ (~.:=\\) o 125

\()~ -\- ~31 428 - \0002 256 3 108

4 83400 A) 0.428 B) 0.125 q 0.553 D) 0.809 E) 0.191-

~suppose that for a certain experiment P(A) =.33 and P(B) = .29. If A and B are mutually exclusive 17) _ ~events, find P(AuB) -33 +,2'1

A) .62 B) .38 q .33 D) .29 E) 0.00

@)For two events, A and B,P(A) = ~, P(B) = ~, and P(A I B) = ~ . Find P(A n B). ....

~~ ~! ql ~! E)l10 _ 9 2 8 3

~The manager of a used car lot took inventory of the automobiles on his lot and constructed the 19) _ following table based on the age of each car and its make (foreign or domestic): p( 0-2- n.c)

Age of Car (in years) . plo-2. Jf) ::.-:......----­\?lr)Make 0-2 3-5 6 -10 over 10 Total Foreign \. 38 22 10 .)u EMD 6~

Domestic 45 26 13 16 100 Total 83 48 23 46 200

A car was randomly selected from the lot. Given that the car selected was a foreign car, what is the probability that it was less than or equal to 2 years old?

A)! B)~ C) 62 D)B. E)~ -::..3<6 _ 505 117 117 50

utAU\3)r;:;;~ 1 1 1 -- (l"\ B' - \-r®Given that P(A or B)=6' P(A) =7' and P(A and B)=8' find P(AnB). t: p \ H U .) \" 20) _

:: \ - ~ 73 5 25 1 31

A) 168 ~ 6 q 168 D) 16 E) 168

~The table lists the smoking habits of a group of college students. 21) _

Sex Non-smoker Regular Smoker Heavy Smoker Total

Man 135 41 5 181 f (""' \JR\ ~ ~ l ~) -*" ~ ( R)- Pl ~f\j Woman 187 21 12 220 _ '<6y btL _ '--'\ ~7 Total 322 62 17 401 - ~c\ : ~ ~ -:: \...\0\

If a student is chosen at random, find the probability of getting someone who is a man or a Regular Smoker

A) 1 B) 0.504 q 0.918 D) 0.803 E) 0.197 -3

~'y~ ;;, An auto assembly worker requires 2 electrical fuses for each vehicle. The supplier of the fuses has informed the plant manager that 6% of all the fuses they produce are defective. Assume that the assembly worker selects the 2 fuses for any vehicle t ran nd . dentl of each

What is the probability that any vehicle will have at least one defective fuse? 22) _

A) .1715 ~<. ,B) .0036 flD) ~ ,ob _' ~ _ \

,...~~ ;~~~4 P \?S- D >,- \\) ~ 1 \~ \:) I D\S ,b D \) ~ l"I\'\lC>\A."'-dI

E).0025 p<...'E') -::: ,C\\\ <_ ~."'''ob~.eb + ~G(;,(!\\.\\ -" .qV\ l,ob) ~ ~~~ y­...'')f@At a~llege! ~2% of students speak English, 5% speak French, and 3% speak both languages. What 23) _

' '~.(p is the probability that a student chosen at random from the college speaks~ [: ~ \ ( 1r A) 0.05 --:-) B) 0.19 C) 0.17 D) 0.24 E) 0.02 ~

p(~(\E ::::;. ,(:)2- ~ • survey of publishing jobs indicates that 92 percent are completed on time. Assume !battW()jobs-~24) _

~o("~o are selected for study. What is the probability. that. they~are all completed on time? .~_:=.~.1/<'0

',~' tOo, ')\M,\l\t~ t: ,~'L1oo!-'''1., "'ti =, o"b ,/ t:I A) 0.4468 B) 0.8464 C) 0.8844 D) 0.1536 ,,\)-.",~

~ It A survey of publishing jobs indicates that 92 percent are completed on time. Assume that two jobs 25) _ ')..'1..- . are selected for study. What is the probability that at least one was not cOIIij'leted on..!!meL. __ \

~ CO' ~ I l s 1 00 ,C> 6 I 0 0

A) 0.1665 B) 0.3526 C) 0.1335 D) 0.1536-\~"

, 'l.-~ ,) 'A survey indicates that 70% of all students live with their parents. Two students are selected at 2~ _ 'l.- . random. What is the probability that at ~st one lives with parents? p'l l ~ I ) L -z: _, <~

A) 0.09 ~ 0.91 C) 0.89 D) 0.93 -e~ \... -:::3 L

@or two events A and B, P(A) :::: 0.60, P(B) :::: 0.40, and P(A IB) :::: 0.90. Find P(B IA) 27) __

A) 0.9 B) 1.0 C) 0.2 *0.60 E) 0.36

P\i\(\{S) "':. .<1",'\ -= ·3~ -1> pCB)"'): '70:: ,f:, study was recently done in which 500 people were asked to indicate their preferences for one of 28) _

three products. The following table shows the breakdown of the responses by gender of the respondents.

Product Preference Gender ABC Male 80 20 10 Female 200 70. 120

~ that a randomly selected person is a fem,\le, the probability that the selected person will prefer product A is:

A) 0.16 B) 0.51 C) 0.56 D) 0.18 E) 0.286 -~.SI3

4

---A study was recently done in which 500 people were asked to indicate their preferences for one of 29) three products. The following table shows the breakdown of the responses by gender of the respondents.

Product Preference Gender ABC Male 80 20 10 Female 200 70 120

Given that a randomly selected person prefer product B , the probability that the selected person is a female is:

A) 0.31. .Jll 0.78 C) 0.86 D) 0.92 E) 0.24.

• uppose that 60% of students at one college drink coffe~d16%of students who drink coffee 30) ~~_ suffer from headache. What is the probability that a randomlj-selected student who drinks coffee"" ~(\-\ IC)~ .\b does not suffer from headache? . ~>.. rJ C' b../

A) 0.76 B) 0.96 C) 0.84 ~.16 E) 0.096r'- "-";~.(. ~ 1<;.) -; .~-~e probability that a new advertising campaign will cre 31) _~_

cost of developing the new ad campaign an be ke t wi . Assuming that the two events are independenJ, the prob ~ the campaign will not increase sales is: ~o~ m~W qo~

®The probability that a new advertising campaign will increase sales is 0.80. The probability that the 32) _ cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, the probability that the cost is not kept within budget and the campaign will increase sales is: PC£ (\ A) ~ b er , %I

A) o.io B) 0.68 q 0.48 D) 0.08 E) 0.32-~e probability that a new advertising campaign will increase sales is 0.80. The probability that the 33) _

cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, the probability that neither the c~ is kept within b budget!!Q! the campaign will increase sales is: 1<':: -PI (\~) = . '2- u,,-,

A) 0.88 B) 0.12 q 0.16 D) 0.32 E) 0.68

~ i· ~ survey of se'~r citizens at a doctor's office shows that 51% take blood pressure-lowering 34) _

medication, 42% take cholesterol-Iowerin medication, and 5% take both medications. What is the probability that a senior citizen tak eithe blood pressure'-lowerin@holesterol-l~wering \:> ( p.,U e) medication? . _ • s \ ~,'V\ 1. - ,cD

A) 0.85 B) 1 q 0.88 D) 0.14 E) 0.90 -­

@A survey of senior citizens at a doctor's office shows that 52% take blood pressure-lowering 35) _ medication, 43% take cholesterol-loW~edicatiOn, and 5% take both medications. What is the probability that a senior citizen takes eithe blood pressure-Iowerin~holesterol-lowering medication? "'CJ

A) 0.48 B)0.13 q 0.15 ~) 0.10 E) 0.57

­ ,.., \

5 i.;".'"

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§A survey of magazine sUbs~showed that during the past 12 months 45.8% rented a car for 36) business reasons, 54% rented a car for personal reasons, and 30% rented a car for both business and ­personahe~s. What is the probability that a subscriber rented a car during the past 12 months for busines~ersonal reasons? l' (Au B)

A) .302 B) .986 C) .866 D) .698-@A survey of magazine subscribers showed that during the past 12 months 45.8% rented a car for 37) _

business reasons, 54% rented a car for personal reasons, and 300 0 rented a car for both business and

personal reasons. What is the probability that a subscrib did no rent a car during the past 12 months for~uSines(Q!'personalreasons? . ,,(AU s, ) ;;., l - VU-\U~).

A) .698· '=-8) .896 C) .998 D) .302-. ~@A multiple-choice test has five questions, each with five choices for the answer. Only one of the 38) _

..>-1-';!,J choices is correct. You randomly guess the answer to each question. rat is the probability that 01: you answer th~question correctly? ~ p""-b' 0 ~~-<-

A) 0.02 B) 0.2 C) 0.4 D) 0.04 E) 0.5 ~ --::;>~

Ailurn contains 5 white balls and 5 black balls. One ball is drawn at random from the urn and then 39) thrown away. A second ball is then drawn from the urn. What is the probability that the second ,s.~ \~

ball is white? \' l "'h C'\ W2.- '\ -\- ~ \. ~\ (\W2.) ~ I B A) 0.45 , B) O.SO) ~ C) 0.54 D) 0.40 10

~ S ~ ~ "" 5/\0 ~ ~ ~ •.5 r 40) A survey indic~s that 30% of college students drink coffee, 72% of college students drink tea, and 40)

( 25% of them drink both. If one student is selected at random, what is the probability that the -- ­student drinks coffeE€fuea! pC C U-t·)

A) 0.77 B) 0.67 C) 0.57 D) 0.87

Hamad and Fahd go to a coffee shop during their lunch break. Each one of them wants to pay. 41) They decided to toss a coin to see who will pay. What is the probability that Hamad will pay 2 \A

d\;'\~ consecutive days? B <.. ~ A) 0.25 B) 0.50 tb \.~C) 0.75~) D) 0.52 . <. .___--­

.- \ H\""\ ::: Y ~ \-\. A ~ \ 2. 1.\ F .......... .~~ 'F

',..,Q~ ® A multiple choice quiz ha~u;estio~each with five answers. If you ~t guess on ~l of the 42)

~ ",,' -i' ~estions, what is the probability that you g.ettil-:!I' a!~_:right? "* q£ .5 ~'" A) 0.04 B) 0.20 C) 0.08 D) 0.16 f ~ --Yrr @} multiple choice quiz has two questions, each with five answers. If you just guess on all of the 43) _

/0..,;"- questions, what is the probability that you get them all wrong? '1s "",. ~ <, "h/ A) 0.44 B) 0.80 ..9.0.64 D) 0.46

<.....{ I ,\""', \..: II I' A basketball team has 10 players. Five are seniors, 2 are juniors, and 3 are sophomores. Two players 44), 0 are randomly selected to serve as captains for the next game. What is the probability that both -- ­

~\.... players selected are seniors? ~ l s, As,,) ~ """~ l?-~' ~ "a"'\. A) 0.25 B) 0.50 ,~0.22'~ ~ D) O.~O ~~ ~

<llllil ~0 ~;;.p ~,~V'j".:--:ilY basketball team has 10 players. Five are seniors, 2 are juniors, and 3 are sophomofes. Two players 45)

are randomly selected to serve as captains for the next game. 'What is the probability that only one. -- ­?f the two players selected is senior? c

~~ ~~ C)~ ~~ S

- .~ C\ ~ \0 ~~ C\~. .y*"~q +10*"(\~j _. lD

/5 6 " $/'" :!> \ "/"",~ .." ~ * / :::::I fr'v\" ~ \0 q

_....!----=----:')(0

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46) An aerospace company has submitted bids on two separate contracts, A and B. The company has a 46) 50% chance of winning contract A and a 40% chance of winning contract H.Furthermore, it believes that winning co~tr~is independent of winning contract B. What is the probability that the ) S company will ~contracts? P(~ 1\6) ~ ~(P\) .. "l~ - '''\ ift"

A) 0.20 . H) 0.25 C) 0.50 D) 0.40 -47) An aerospace company has submitted bids on two separate contracts, A and B.The company has a 47)

50% chance of winning contract A and a 40% chance of winning contract B.Furthermore, it believes that winning contract A is independent of winning contract B. What is the probability that the company will win at least one of the two contracts? ~ \~'.)\?'\

A) 0.75 U B) 0.90 C) 0.37 D) 0.70-48) An aerospace company has submitted bids on two separate contracts, A and B.Suppose that the 48)

aerospace company believes that it has a 60% chance of winning contract A and a 30% chance of winning contract B. Given that it wins contract H, the company believes that it has an 80% chance of -- r(~\e).::; , <6winning contract A. What is the probability that the company will win ~th contracts?

A) 0.48 B) 0.24 .... C) 0.42 D) 0.18 . .3> - '~ Pl f\(\B)::; . '8' It" •

49) An aerospace company has submitted bids on two separate contracts, A and B.Suppose that the 49) aerospace company believes that it has a 60% chance of winning contract A and a 30% chance of winning contract H.Given that it wins contract H, the company believes that it has an 80% chance of winning contract A. What is the probability that the company will win at least one of the two . r» 'LS contracts? U . -=: \~~ ... 21 -,

A) 0.'7.7 B) 0.66 C) 0.70 D) 0.61

"An aerospace company has submitted bids on two separate contracts, A and B. Suppose that the 50) _

aerospace company believes that it has a 60% chance of winning contract A and a 30% chance of winning contract B. Given that it wins contract B, the company believes that it has an 80% chance of winning contract A. If the company wins contract B, what is the probability that it will not win contract A?

A) 0.32 B) 0.80 C) 0.20 X'D) 0.66 o ( A' \3 ) . .... p(rd\3).:::'-~ \,..,~;:;.2..

G~ The employees of a company were surveyed on questions regarding their educational background 51) and marital status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single and had degree The probability that an employee of the company is a married is:

A) 0~10 g uVea; B) 0~833 C) 0.25 D) 0.733 E) 0.667 '\ ....... - \1::)0

P\.~l ;:P\.S)~ '---.v The employees of a company ~?e surveyed on questions regarding their educational background 52) and marital sfatus. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single and had degree. The pro~~bility th~t an employee of the company is married and does not r \.tu'" Iv'" 6<> have a college degree is: pt !i n c ) -= K s;: \J c. ') -z \ - \>l$ U C ') :::. 1- L~ -\- be"6-.::;­

rA) 340/600 .!~ 500/~ yo C) 400/600 D) 40/600 E) 160/600

~~~~~~ ~-lfThe~ployeesof a company were s~yed on questions regarding their educational background 53) __

and marital status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single and had degree. The probability that an employee of the company does not have a colle~

degree giventhat he is a single is: . A) 0.40- B) 0.75 C) 0.33 D) 0.10 E) 0.67

- y{Cs>4Y: 'J,

WU>~600 - 1­

, ~- ~I~ S~ 11\ ' ~ \ I s £3 '3 \ If) A group of volunteers for a clinical trial consisr5''Of-81-wom~77 men. 18 of the women and 19 54)

of the men have high blood pressure. If one of the ~o1.unteers is l§"lIected at random find the ~---probability that the per~n has high blood pressure given that it is a man. pC~ I H) .=- 11

A) 0.486 CIDJO.247 C) 0.356 D) 0.222 E) 0.114 f

~ (1'55) A group of volunteers for a clinical trial consists of 83 women and 78 men. 21 of the women ~d 2055) L- of the men have high blood pressure. If one of the volunteers is selected at random find the \ ~ \ -2-,- ­

i-O Sg ., ~r~l~~:bllitYthatthe person lsawoman given that they have high blood pressure. ' p~ .' :; 2.1 62 ~3. @.512 B) 0.488 C) 0.256 D) 0.247 E) 0.124 Y I

~~~~..;tirOfl0(j'cD;;;;;'~~;';;;d';;;~:"';'C::~~~~-;;::-i.5~ty~f the total CDs~.;k156; ~ .i'l.'P' manufactured on machine, I, and 10.of these 60 are defective. One CD is selected randomly from ~ ~ ~ (::;>0

+.k:~(~(-~ t~ese 100 CDs. Wha~, is ~e probability that this CD is defective? \'0») ~ ~ ~ ~ t;\) ~ ~ ">..=:., \1:' S'" ...\'@0.20 ~ 7{'Y-- ,B) 0.60 C) 0.30 \10 '\,.P) 0.50 .e _ 60

, \00 • 0 0 illD" i l!:l 6o...l. _ <- ~ ~ 1.\0 I')) J,J ~ I.£­. ..;> ~oJ ' ):::.. 60 - I 'L\I.:)!.fi) ~ ~ '''( y 0

~ti) Of a total of 100 CDs manufactured on two machii1es,20 are"cfefective. Sixty of the total CDs were 57) 81­ft-: ~ manufactured on machine I, and 10 of these 60 are defective. One CD is selected randomly from •t1 ~

( .:.;x) these 100 CDs. What is the p~,Q,abilitythat this CD is defective &anufactured on machine I? ~) / "to .f>e,"J A) 0.20 ~.10 C) 0.30 '~ D) 0.50 ~ \ {( r'\ , ~ ~ • ~ ~ (00 /(;,,) I""",

\ A Of a total of 100 CDs manufactured on two machines, 20 are defective. Sixty of the total CDs were 58) _ ~ manufactured on machine I, and 10 of these 60 are defective. One CD is selected randomly from )

i'J-i'0" these 100 CDs. What is the probability that this CD is defective given that it was manufactured on L t>\ s:. \- machine I? f '\ to

A) 0.176 B) 0.771 C) 0.617 @0.167 ~

Of a total of 100 CDs manufactured on two machines, 20 are defective. Sixty of the total CDs were 59) manufactured on machine I, and 10 of these 60 are defective. One CD is selected randomly from . ~::-,""")--­

these .100 CDs. What is the f!rO~~.bili.ity th~.~ ~.~is CD is ~eitl},{r defecl~ nor manufactured on l~C (\ machine I? ~ l,. l ')'i:;;'~ ~ \'~7~? ".~; ~\ .) ~ I"!"\ Q

A) 0.10 B) 0.50 . 0.70 lJ,J,f'0.30" ~'l r) .. \' ( , ,,,,.,~, ..,~,,~.,~"" _~","~'"., ." ~ r( ) :: \.- ~ ( tJ \.J r ) == \- L ~ t r~ ) " ~ - ,

"'l.}J'(J) There are 200 students iri a~paifiCuIafgfaduate-programara~stafe~umversHY:'nfThem,nOare' -~-_.'60) . - ­( ) female and 125 are out-of-state students. Of ~e 110 females, 70 are out-of-state, students. . -s:

a. If one of these 200 students is selected at random, what is the probability that the student selected -l::'---r \\\j is ~ale? f (t"') ';; ~~~ 5r (§0:45 B) 0.54 C) 0.55 D) 0.40

, -----~-::::~ ~ 61) There are 200 students in a particular graduate program at a state university. Of them, 110 are

female and 125 are out-of-state students. Of the 110 females, 70 are out-of-state students. If one of (r -:\0 these 200 students is selected at random, what is ,the probability that the student selected is an ~ D \ Q:'"\ __ o~-state student given that this student is a female? ~ \.. \ \0

~.6364 B) 0.560 C) 0,6643 ' D) 0.7634 ,

62) There are 200 students in a particular graduate program at a state university. Of them, 110 are 62) _ female and 125 are out-of-state students. Of the 110 females, 70 are out-of-state students. a. If one of~se 200 students is selected at random, ,,;hat is the probability that the student selected is a femal~ut-of-state student? ~

A) 0.528 B) 0.805 \s.p0.825 '[») 0.558 '\ ~

r ·O\·~ ~ k \~ - ~ VC" \J J ?JiJu ?[vJ

8

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63) _

~-~~------------------65) Som}\~~nd women were surveyed for their marital status. It was found that 16 were unmarried 65) _

~'(p, mal~s~4 were married males. In the whole sample of 90 persons, 34 were unmarried. Answer ~ _ ~ the following questions. Compute P(male or married) f(~ t..J 1'1"\". \ = ':? ---.,;M-'l!..I:.--.i_

A) 0.80 B) 0.85 C) 0.90 D) 0.77 \-.-\ 3"\ \6 so ~ •. 1 n~ \~ 40

-=VV~~·L.;i1'-'\0.y66) Some men and women were surveyed for their marital status. It was found that 16 were unmarried SA) 1~

( males and 34 were married males. In the whole sample of 9£~ersons, 34 were unmarried. Answer the following questions. Comp~te P(male Imarried) ~ ~

A) 0.760 B) 0.393 . . C),0.680- D) 0.607 i

67) Some men and women were surveyed for their marital status. It was found that 16 were unmarried 67) males and 34 were married males. In the whole sample of 90 persons, 34 were unmarned. Answer the following questions. Compute P(male and marrie~) ~ (~ (\ ("t\c ) 3}1q o

A) 0.178 B) 0.378 C) 0.244 D) 0.200 ~ "'It.....

~c:t:>,.2 \-,;> t~ 55 percent of students ~re females. 80% of the females love math, while 0;"1 60% of the mal~s love 68) L L.._

~Lr ,:Vmath. What percentage of the students love math? L S. ~ ,~~/,r,~ A) 0.29 B) 0.44 C) 0.71. .0.\.\ .,, A> D) 0.27 \-\ \ .1.-1,~ .11 ,\ 'b .

69) A company has 2 machines that produce bags. An older machine proJ~ce~ 23 Yo defective bags, 69) _ while the new machine produces only 8% defective bags. In addition, the new machine produces 75% of the bags and the older machine produces 25%of the bags. Given that a bag was produce~

by the old machine, what is the probability that it is not defective? \ pl e>tl,,) , . .: ,~ ~ A) 0.94 B) 0.06 C) 0.77 D) 0.50 I E) 0.92 ,lJ

\

IT' 70) A company has 2 machines that produce bags. An older machine produces 23%defective bags, 70) __ I while the new machine produces only 8% defective bags. In addition, the new-machine produces

75% of the bags and the older machine produces 25%of the bags. What is the probability that a randomly chosen bag produced by the company is not defective? ' ~~~

A) 0.078' B)0.310 ..~.... QO.156 ~_.D)'Jl'P75 ~cn E) 0.8825 (6) • ,'" Y-~~) -T' • 9L~ :15) "" - f'

71) A company has 2 machines that pro u 'ba:gs:,An older machiit 0 uces 2~% defective bags, 71) .....,'--0>":­

while the new machine produces only 8% defective bags. In addition, the new machine produces . \ ..~

75%of the bags and the older machine produces 25%of the bags. Given a randomly chosen bag .p l ~o \ P J': ­was tested and found to be defective, what is the probability it was produced by the old machine? . '- \~

A) 0.115 B) 0.08 C) 0.15 ~ 0.4~ ~11

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Use Bayes' theorem to solve this problem. A storeowner purchases stereos from two companies. 72) From Company A, 250 stereos are purchased and 1% are found to be defective. From Company B, 950 stereos are purchased and 10% are found to be defective. Given that a stereo is defective, find the probability that it came from Company B.

1 19 10 D)~ E) 38 A) 39 B) 195 C) 39 39 39

~

1t,. Use Bayes' theorem to solve this problem. A storeowner purchases stereos from two companies. 73) _

From Company A, 600 stereos are purchased and 12% are found to be defective. From Company B, (1 750 stereos are purchased and 6% are found to be defective. Given that a stereo is defective, find the probability that it came from Company A.

10 4 5 A) 13 B)13 C)13

0\13

Answer Key • ,A

Testname: EXERCISES FOR PROB (CH.4) STAT 120 FALL-2012-2013

51) B 52) E 53) A 54) B 55) A 56) A 57) B 58) D 59) D 60) A 61) A 62) C 63) D 64) C 65) A 66) D 67) B 68) C 69) C 70) E 71) D 72) E 73) D

12

Answer Key Testname: EXERCISES FOR PROB (CH.4) STAT 120 FALL-2012-2013

1) E 2) C 3) C 4) A 5) B

6) A 7)C 8) B 9) A

10) A 11) A 12) C 13) C

14) ~Mi kr4.m~~~~. E 15)A 16) E 17) A 18) B 19) E 20) B 21) B 22) D 23) E 24) B 25) D 26) B 27) D 28) B 29) B 30) C 31) C 32) C 33)B 34) C 35) D 36) D 37) D 38) B 39) B 40) A 41) A 42) A 43) C 44) C 45) A 46) A 47)D 48) B 49) B 50) C

11

'Exam: The Second Midterm Exam Stat 120 20 questions 20 Points 60 minutes

Name ill: Instructor: Sec:

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

*' (D)For the following statment:: "the probability that a newbom baby is a boy is~" . state whether 1)

this statment is an example of classical probability, empirical (Relative frequency) probability, or subjective probability.

A) subjective probability B) empirical (Relative frequency) probability ~as~calprobability D) all of the above E) none of the above

-+@If two equally likely events A and B are mutually exclusive, what is the probability that event A 2) occurs?®Cannot be determined from the information given. B) 0.0 C) 1.0 D) 0.5 E)none of the above

*' ~ 3)The expression peA('\B) =P(A)P(B IA) is valid: @,for any events A and B.

B)only if A equals B. C) IfA and B are independent. D) If A and B are mutually exclusive. E) nee of the above

~ ~ P(A)=0.8,P(B) =0.1, and P(A and B) =0.07.Classify the events A and B as: mutually exclusive, 4) _

dependent or independent: I"l "\ l p..,\ \. ,~) I:J independent pt P\ (\ \~) * \' ' ~

(i))fependent 'c)mutually exclusive D) both A and C E)both A and B

8-1

. 0"<; "... ( r: 1\ I .1-- I • ~ 20 cJ~JJ'6\ u: <;::,j:),

~@yarlk the following three probabilities: 10%,i, and 0.06 from ~':..m~~ likely to oc~ to tte leafrt 5) _

likely to occur.

fA))!.~5' 10%, 0.06

B) 10%,i, 0.06

C) 0.06,i, 10%

D) 0.06, 10%, i E) 10%, 0.06, t

"*@rwo events with non-zero probabilities 6) _ @lcannot be both mutually exclusive and independent

B) can be both mutually exclusive and independent oe C) are always mutually exclusive )( D) are always dependent l(

E) both b and c

J~ @In a class of 40 students (18 females and 22 males). Randomly select two students without ""i' replacement, what is the probability that both of them are male?

A) 0.7038 B) 0.1962 C) 0.550 D) 0.3025 @.b.2962

2L '2 \ f((1'), n,0" -c) . ~ -- ::.. ''2. (\ t \Cj :: .'7. q [,'I" '-t C· .5 c\

. ®n a class of 40 students (18 females and 22 males). Randomly select two students without 8) _

...:1< replacement, what is the probability that at least one ofthem is a male? A) 0.2962 . @0.8038 - 'C) 0.5077 'D) 0.1962 E) 0.7269

c\:'\ \ <us. \'1 (YI: 0"'. J1.." Q' lYl \ (n 'L \, ~n_ 1. '''') () (

7('. ..J\f',r.,) ..._ ,~ ,.,' '-.., . '. ., . b ,'/.2- l) I _ ,,0) (1:\.,t....·J \ \"~... ..!::..!= • \'t. 1)( [fl('I)) :;:_1.-.(7

L.tCi ~ Y,- 11 <. l-Jc 3"'\ i ,'I \ . ­

- 3'1

~e probability that it rains saturday is 0.66 and the probability that it rains sunday is 0.49.The 9) _..¥ probability that it rains both days is 0.23. What is the probability that it rains exactly (only) one ~? (Hint: you may use Venn diagram to solve)

A) 0.43 B) 0.17 C) 0.69 D) 0.26

LICI_ .2';.\

.--. ~9

B-2

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J2=­~ ~ 2c:>?>8 *~

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,J.,.. @>Suppose the probability that Fahad passes the statistics exam is 0.70. the probability that Hamad 10) _

'" and Fahad both pass the statistics exam is 0.24.The events Fahad and Hamad passing are independent. What is the probability that Hamad passes?

A) 0.168 B) 0.232 @.343 D) 0.94 E) 0.46

peF) -=·1­I

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Table 3

Teachers <n Men(M) 15 55 Women(W) 25 45

40

*' @USing Table 3, the probability that a person is a woman, given that the person is not a teacher is 11) _

A) 25. B) 20 . C) 25 rD~) ,20 E) 25 40 100 45 ,,-':!60' 100'

?\ \N \ S )

-.L. @A short quiz has one true-false question and one multiple-choice question with 5 choices. A 12) I" student guesses at each question. Assuming the choices are all equally likely, what is the

probability that the student gets all two questions correct? 1 r;;';) 1 1

A)Z ~ C)s

\ .-\-" ~­)7­

Exhibit 1 f f l :) ::- . h \X-.. S) ::-. 0 4

"' ( f:.:; ) -: u- . ,~ J'if.1\ \ _ .,l --' - - . \ "p I::=J !l~"l ./ - (" .~<!I

In a meat packaging plant Machine A accounts for 60% of the plant's output, while Machine B accounts for 40% of the plant's output. ~ 4% of the packages'are improperly Seale<!. Also, 3% of th~packages are from Machine A~~.~r~ improperly sealed. . ../

@>Referring to Exhibit 1, if a package is selected at random, the probability that it will be properly 13) _

d< sealed is . . ~ . A) 0.05 B) 0.03 . . C) 0.96 D) 0.12 @.04

01 peS'I A) :: ----:r;;

N... @Referringto Exhibit 1, if a package selected at random came from MachineA, the probability that it 14) _ J"- is improperly sealed is . "

A) 0.04 B) 0.60 @.05 D) 0.12 E) 0.03

vc(-'c'" 22­r.::\,., PCf'or/5):: ,"co,)

. ~eferring to Exhibit 1, if a package selected at random is improperly sealed, the probability that it 15) _ "j-:. came from machine A is .

A) 0.60 C) 0.40 D) 0.03 E) 0.04 @.75

B-3

1 a suvey of the number of DVDs in a house, the table shows the probabilities.� NumberofDVDs 0 1 2 3 4 or more� Probability 0.05 0.24 0.33 0.21 0.17�

1,... @ind the probability of choosing a house that have 1 or 2 DVDs. 16) _

l' 00.57 B) 0.95 q 0.67 D) 0.83 E) 0.38

pC Y.. ~2- ) k" ~ l "1..-= ~) ~. 'L ~ -\ - ~:!:>

@Find the probability of ~ossing a house that have 3 or more DVDs. 17) _

A) 0.57 ~0.38 C) 0.05 D) 0.17 E) 0.83

"("1-.. //3 ) ~ \')(1-.. -::~) "' ~ \~:: t:\) ~~ .. 2-\ ~,\"'1

;::4<. ~ the coffee makers sold in an appliance store, 4.0%have either a faulty switch or a defective cord, 18) _ ~.5% have a faulty switch, and 0.1% have both defects. What is the probability that a coffee maker

L~r"? will have a defect!ve c~rd? Express the answer as a percentage. ? A) 4.1% B) 2.6% @1.6% D) 4.0% E) 6.4%

~ (~ o D) -:: .0"\ (\ ~ \}\J') -:: ~~ f) -t pCDJ - ~ C. t" (\\)J (' <.. ~) ::. • c'l-S . o '" z: ,\)1...S -T sp<. \~J - \0 0 \ \ ~

p( E;;~~. ') :; • O~\ ('<..~) "'-' o ®,wo grotrps of people were asked their preference in television programs from among three new 19) _

;\<-. programs. The resultsare shown in the table below. What is the probability that a person selected at :andom will be from group A or prefer program X?

Television Program z

40

50

l-I" 1<; A) 0.371 B)0. 874 (9)J.476 D) 0.152

~The probability distribution for the random variable X is: 20) _

p Xi -1 0 1 2

Pi 0.22 0.23 0.26 0.29

What is the expected value of X? A) 0.26 ®0.62 C) 0.54 D) 0.50 E) 0.22

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B-4