math final
family 5 children with probability of having a girl is 1/2, probability of having 2 girls followed by 3 boys.
.0313
pay $1 to roll fair die to get back $3 for rolling 4 or 2
A) $0
fair coin tossed three times and player wins $3 if 3 tails occur. wins $2 if 2 tails occur and loses $3 if no tails occur
A) $0.75
n = 62, x= 26, 95 percent
A) (0.297, 0.542)
33% of physics majors belong to ethnic minorities. 10 students are physics majors: seven or more belong to ethnic minority
A) .0185
5 apples in a barrel of 25 apples rotten. sample of 2 apples.
A) .4
81% of scheduled flights and cancellations indepndent events.
A) .53
probabiltiy of at least 2 students in a class of 36 hav same bday
A) .832
coin is tossed 4 times. possible values of random variable x
A) 0,1,2,3,4
california lottery. game of super lotto. probabiltiy of choosing 3 of 5 winning numbers but not mega
A) 0.005
out of 230 trials, 110 turn out pos.
A) 0.0646
people are catching cold. 40% of people are sick . 30% sick after one week (no matrix)
A) 0.332
M = 0.9, 0.1, 0.1, 0.9, s 0 = 0.3, 0.7. s2=?
A) 0.372, 0.628
Cumberland County, 55% democrat. 30% republicans, 15% independent. 35% democrats. 65% republicans. 75%indepndent.
A) 0.385
p(a) = 0.1, p(b) = 0.2, p(c) = 0.4, p(d) = 0.3. p(a,d) =?
A) 0.4
high moderate low table with #'s 0.12, 0.25, 0.05: find the probability a male is selected
A) 0.42
sunny cloudy weather (0.7, 0.3, 0.4, 0.6)
A) 0.571, 0.429
stop n' go tune up and brake shop. 0.6 tune-up, 0.1 brake, both 0.02
A) 0.68
rats kept in cage with A and B. Rats in A move to B with 0.1. Rats in B move to A with 0.5.
A) 0.833, 0.167
assembly line operation. 0.91 chanc eline will work. 0.68 line will not work.
A) 0.883, 0.117
out of 30 job applications, 11, 17, 7, 3, 6,2; the number of female college graduates who are not bilingual is
A) 1
coffee makers. 4.0% either faculty swtich or def cord. 2.5% faculty switch. 0.1% have defects.
A) 1.6%
five horses running. son-of-a-gun
A) 1/20
three coins are tossed and number of heads is noted
A) 1/8, 3/8, 3/8, 1/8
new light bulb have 0.02 of being defective. a shop owner 500 bulbs
A) 10
in a group of 42 students, 22 take history, 17 take biology, 8 take both history and bio. how many students take neither bio nor history?
A) 11
box contains 7 red, 3 green, 5 blue
A) 11/15
45min tours from 10AM - 3 PM; in how many ways can the traveler visit all three places in one day?
A) 120
art department of two oil paintings, two watercolors, and two photographs. 8 op, 6 wc, 10 photos
A) 151,200
group of 5 boys and 6 girls: how many ways can 5 children with 3 boys on left and 2 girls on the right?
A) 1800
in how many ways can 8 people be chosen and arranges in a straight line, if there are 12 people from whom to choose?
A) 19,958,400 ways
steady state matrix for 0.1, 0.9, 0, (3x3)
A) 2/9, 4/9, 1/3
a bag contains 5 apples and 3 oranges. if you select 4 pieces of fruit without looking, how many ways can you get 3 apples.
A) 20 ways
mr cameron sponsoring summer concert. 300,000 not rain and 60000 if it does rain. 150,000. 30,000
A) 239,400
45min tours from 10AM - 3 PM; in how man ways could the traveler schedule two of the three tours in one day?
A) 30
between z=-2.35 and z=-.14
A) 43.5%
2598960 diff 5 card-hands: all four jacks
A) 48 hands
8 roads connecting from A to B; 6 roads connecting B to C. in how many ways can a person travel from A to C via B?
A) 48 ways
a bag contains 5 apples and 3 oranges. if you select 4 pieces of fruit without looking, how many ways can you get 4 apples.
A) 5 ways
toss 6 fair coins. obtains at least two heads
A) 57 was
toss six fair coins, obtains at least two heads
A) 57 ways
license place consist of two letters followed by 4 digits: repetition is allowed
A) 6,760,000 licenses
license place consist of two letters followed by 4 digits: repetition of numbers and letters
A) 6,760,000 licenses
n(A) = 33, n(B) = 19, and n(AnB) = 1, n(A´n B´) = 9. Find n(U)
A) 60
software company, 9 sales rep, 8 tech rep. needs at least 4 tech rep
A) 686
male decreases his life expectancy by 1 year on average. above 120. average life expectancy is 76 years. blood pressure is 127
A) 69
human resources director 9 people for entry-level position. two highly qualified, 5 qualfiied, 2 unqualified.
A) 756
how many ways can a group of 8 students be selected from 9 students
A) 9 ways
Find A (diagram: A = 9,2; B = y,f,q)
A) 9, 2, 5
how many 6 digit numbers can be formed using the digits 0-9, if repetitions of digits are allwoed
A) 900,000 six-digit numbers
experiencs how ski lodge (158 guests), partially full (56 guests) with light snow fall. .40
A) 96.8
if a = 1,3,5,7; b = 5,6,7,8; c =5,8; d = 2,5,8, what is C (symbol) D
A) True
(11,33,38)___(5,33,38,48)
A) crossed out!
disjoint or not disjoint: A´n B´
A) disjoint
mary has flue and dcotor viruses. 2x2 matrix (.75, .35, .45, .55
A) medicine 2; 4/5
(c,d,i,g)___(c,d,i,g,m)
A) not crossed out
bag contains 5 red marbles, 6 blue marbles, 2 green marbles. find blue
A) p(b) = 6/13
p(a) = 0.3, p(b) = p(d), p(a) = p(c). find p(d)
A) p(d) = 0.2
if u = q,r,s,t,u,v,w,x,y,z; a = q, s, u, w, x, y, z; c = v, w, x, y, z, A (n) B´
A) u,w
p(t) = 0.2, p(q) = 0.2, p(r) = 0.6. valid or invalid?
A) valid
jane will buy five tapes.
A) valid -- law of detachment
tom goes to the game, dick go to the game, harry go tot he game
A) valid -- syllogism
Find A´ (n) B´ (diagram: A = 7,3; B = z, p ,g)
B) (cross out) o
field goal kicker, average of .75. 3 field goals and field goals is counted.
B) .016, .141, .422, .422
95% margin of error: 186 observations, 75 positive outcomes
B) .0707
on hospital floor, 16 patients have disease w mortality rate of .1
B) .275
calculator keystroke assembly and logic circuit. 85% and 80% satisfactory
B) .6800
homicide case, 3 different witnesses. 5 men, 3 witness pick the same person
B) 0.04
people are catching cold. 40% of people are sick . 30% sick after one week (matrix?)
B) 0.4, 0.6, 0.3, 0.7 *matrix
incidence of certain disease on Tukow is 4%. 91% of those who have tested positive. 4% of those who have flase positive.
B) 0.487
1000 tickets sold for a raffle that has 1 $300 prize, two $100 prize, and one hundred $1 prizes
B) 0.60
three cards drawn. number of king is counted.
B) 0.7826, .2042, .0130, .0002
basket contains 5 red balls, 4 white, 4 blue. find 2 white balls.
B) 1/11
4 children: 2 girls and 2 boys
B) 1/16
1 blue, 3 white, 2 green, 2 red: both marbles are red
B) 1/28
a single fair die rolled. number is 3 or 4
B) 1/3
1 blue, 3 white, 2 green, 2 red: one marble green and one marble red
B) 1/7
206 employees, 17.48% of carpooling. 90% confidence interval
B) 13.1% < p < 21.8%
out of 30 job applications, 11, 17, 7, 3, 6,2; the number of male college graduates is
B) 14
5 people are selected. 8 freshman and 7 soph. probability of 2 fresh and 3 soph
B) 140/429
if n(A) = 6, n(B) = 13, and n(AnB) = 4; what is n(AuB)
B) 15
home cooking equipment employs 7 sale rep and 6 product designers. selects 4 of employees and at least 3 product designers
B) 155
home cooking equipment, 7 sale rep, 6 product designers. 4 of employees and 3 product desginers. Oahu
B) 155
right-handed father. 90% right handed 10% left. 30% right, 70% left.
B) 16%
computer store 10 copies of word proessing, 12 copies of spread sheet, 8 copies of draw. three of word processing, 4 of the spread sheet, and two of draw programs: a spreadsheet program infected w virus
B) 2/15
table under 18 years of age, diet cola, root beer, lemon- drop
B) 2/5
average weekly income of teachers $390 with standard deviation of $45. $425 a wekk
B) 22%
mathematics instructor 24 students into groups of 4 to work on project. each group works on different project
B) 24! / (4!)^6
toss a coin 7 times. the number of sequences of heads or tails is
B) 2^7
license place consist of two letters followed by 4 digits: no rep of numbers and letters
B) 3,276,000
license place consist of two letters followed by 4 digits: no repetition is allowed
B) 3,276,000 licenses
(diagram: A = 9, 1, 4, 6; B = 3, 4, 6, 2). Find n((AnB)uC))
B) 31
if you toss five fair coins, how many ways can u get 1 head
B) 31 ways
group of 5 boys and 6 girls: how many ways can 5 children with 3 boys on right, 2 girls on left or 2 girls on right and 3 boys on left?
B) 3600
a musician plans to perform 9 selections. in how many ways can she arrange the musical selections
B) 362,880 ways
average size of fish in lake 11.4 inches. with standard deviation of 3.2 inches.
B) 4%
how many ways can a committee of 4 be selected from a club with 12 members
B) 495 ways
ATM keypad has 10 keys, 4 keys: if at least one key pressed more than once in a code
B) 4960
an ATM 10 keys, PIN 4 keys: at least one key pressed more than once
B) 4960
an exam contains 5 multiple - choice questions, each having 4 possible answers. in how many different ways can the exam be completed?
B) 4^5
instead of 5 positions, company has 3 positions w no restrictions on college majors
B) 504 ways
ATM keypad has 10 keys, 4 keys: if no key is pressed more than once in a code
B) 5040
BASEBALL (permutation)
B) 5040
an ATM 10 keys, PIN 4 keys: no key pressed more than once
B) 5040
basketball player previous attempt. .55. missed attempt is .48. 45% of attempted.
B) 52%
2598960 diff 5 card-hands: all red cards
B) 65,780
a pollster wants to minimize effect. cover all possible arrangements if there are 6 questions on survey
B) 720
survey 41% of reading books, 48% watching tv, 11% both books and tv
B) 78%
two wally-world. below 50% each gets shown in payoff matrix. 3x3 matrix (12, 8 ,11)
B) 8
eight horses are entered in a race. in how many ways can they cross the finish line if ties are not allowed?
B) 8 x 7 x 6 x 5 x 4 x 3 x 2
bag contains 19 balls 1-19. even number
B) 9/19
company considering two deals. deal a has 0.70 of making 25,000. 0.10 of losing 10000. 0.60 making 30000
B) Deal B
if a = 1,3,5,7; b = 5,6,7,8; c =5,8; d = 2,5,8, what is U (symbol) A
B) False
if george goes to the market, then buy milk
B) indirect reasoning
which can be a prob distribution for X
B) k: -2,0,1,k pr(x=k) 1/3, 5/12, 1/4
disjoint or not disjoint: O n E´
B) not disjoint
a class has 10 boys and 12 girls. committee of 4 be selected if committee have at most 2 girls
B0 4620 ways
n=118, x=66, 88 percent
C) (0.488, 0.63)
10-question multiple choice has 4 possible answers for question. 6 correct answers
C) .020
14% of people business executives, 26% business executives drive cadillacs.
C) .04
four coins tossed and number of heads is counted
C) .0625, .25, .375, .25, .0625
33% of physics majors belong to ethnic minorities. 10 students are physics majors: two or less belong to ethnic minority
C) .1080
die rolled 20 times and number of twos: more than three twos
C) .433
out of 30 job applications, 11, 17, 7, 3, 6,2; the number of women who are not college graduates but nevertheless are bilingual is
C) 0
clinical test with 2153 subjects, 1284 showed imporvement
C) 0.0207
3.9% of secluded island trible 92% of positive disease. 4.4% of false positive
C) 0.078
(a, b, c, d) p(a) = 0.1, p(b) = 0.3, p(c) = 0.4, p(d) =
C) 0.2
p(b) = p(c), p(a) = 3p(c), p(b)=
C) 0.2
samanth taking 0.4 math , 0.6 english. passing at least one = 0.8
C) 0.2
two marbles drawn from bag. 4 red marbles, 2 blue marbles.
C) 0.4, 0.53, 0.07
steady state matrix for 0.1, 0.9, 0.6, 0.4
C) 0.4, 0.6
No..1.2.3, frequency 94,88,53 table: buys no.2 or no.3 seller
C) 0.600
shipment 1 has 2%, shipment 2 has 5%.
C) 0.714
high moderate low table with #'s 0.12, 0.25, 0.05: find the probability a person is selected of moderate or low risk
C) 0.80
two balanced dice are roll. possible values of random variable y
C) 1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,30,36
box contains 8 light bulbs, two of which did not work. probability of selecting both that do not work is
C) 1/28
ATM keypad has 10 keys, 4 keys: if a key be pressed more than once in a code
C) 10000
an ATM 10 keys, PIN 4 keys: pressed more than once in a code
C) 10000
CRITICS (permutation)
C) 1260
jeff, karen, lyle, maria, norm, olivia, paul: in how many ways can the men be presented first and then the women?
C) 144
4 accounting, 2 economic, 3 marketing: 2 accounting majors, 1 economics major, 2 marketing major
C) 144 ways
4 accounting, 2 economic, 3 marketing: there is no restriction on the college majors hired for the five positions
C) 15,120 ways
project manager 12 employees. divided into four groups of three
C) 154000
out of 30 job applications, 11, 17, 7, 3, 6,2; the number of applicants who are either female or bilingual is
C) 16
urn contains 6 red balls and some black balls. number of black balls is
C) 16
fish in a certain lake that is inedible. 99 percent confident of inedible fish 0.01
C) 16,588
license plates are made using 3 letters followed by 3 digits. how many plates can be made if repetition of letters and digits is allowed?
C) 17,576,000 plates
group of 5 boys and 6 girls: how many ways can 5 children with 3 boys on right and 2 girls on the left?
C) 1800
1 blue, 3 white, 2 green, 2 red: second marble is red, given white
C) 2/7
die rolled 20 times and number of twos: exactly four twos
C) 202
word problem: SSU, 399 students taking finite mathematics or statistics, 238, 184, 23
C) 215
federal government estimate proportion within 0.007 with 97% percent
C) 24,028
word problem: EZU, 509 taking college allebra or calculus, 244, 338, 73
C) 265
how many three-letter words can be formed allowing repetition of letters
C) 26^3
computer store 10 copies of word proessing, 12 copies of spread sheet, 8 copies of draw. three of word processing, 4 of the spread sheet, and two of draw programs: infected with a virus?
C) 3/10
numbers 1-20. probabilityy the number is a multiple of 3 is
C) 3/10
3 members of the young democrats on certain college campus
C) 30! / 27!
TENNESSEE (permutation)
C) 3780
(diagram: A = 9, 1, 4, 6; B = 3, 4, 6, 2). Find n (AuB)´
C) 39
If n(A) = 15, n(AuB) = 43, and n(AnB) = 11; what is n(B)
C) 39
coin shows 41% heads and 59% tails. coin tossed twice.
C) 41?
one of the following is false; indictaed by letter which one
C) 5 (symbol) 3,4,5,6
box contains 4 red and 5 green. 3 balls and probability w 2 red and 1 green is
C) 5/14
jeff, karen, lyle, maria, norm, olivia, paul: in how many ways can the people be presented
C) 5040
8 candidates running for 5 positions as judges on supreme bench. the number of possible outcomes is
C) 56
how many three-digit codes can be formed using the digits 0-9 if the last digit cannot be 0 or 1 and repetition of digits is allowed
C) 800
P (8,5)
C) 8x7x6x5x4
car agency found daily demand (.1,.2, .4, .2, .1)
C) 9
chorus has 6 sopranos and 8 baritones. need at least one soprano
C) 931 ways
television set with a mean of 36 years and a standard deviation of 8 years.
C) less than 20.95 years
p(a) = 0.4, p(b) = 0.2, p(c) = 0.5. valid or invalid?
C) not valid
male, 342, 424, female, 324, 102, total, 666, 526: student is female and ed degree received
C) p(f l e) = 51/263
(p-->q) ^ (~q) --> (~p)
C) valid -- indirect reasoning
(6,2,1,4) optimal strategy for C is
D) (2/7,5/7)
(6,2,1,4) optimal strategy for R is
D) (3/7, 4/7)
the set of A (n) A´
D) (cross out)o
game payoff matrix (1,-2,-3,0). R = (0.4,0.6). C = (0.3,0.7)
D) - 0.98
2x3 matrix. find value (-10, -2, -1)
D) -58/13
fair coin is tossed 5 times. probability of no heads
D) .0313
33% of physics majors belong to ethnic minorities. 10 students are physics majors: exactly 2 belong to ethnic minority
D) .1990
500 coins are tossed: more than 239 heads
D) .826
find z score 4% total area is to the left of z
D) .84
all queens in a five card hand
D) 0 ways
95% margin of error: 3000 TV viewers, 900 said they watch network news
D) 0.0164
quality motors has three plants. plant 1 35%. plant 2 20% plant 3 45%/ 2% output of plant 3 is defective
D) 0.224
mp3 players. store a has 34$ of sales. 5% of defective. 66% of sales. 1% of which are defective.
D) 0.2797
p(1) + p(2) + p (3) = 0.7, p(4) = p(5), p(1) = 2p(3) = p(2)
D) 0.28
No..1.2.3, frequency 94,88,53 table: buys no.2 seller
D) 0.374
table under republican democrat stronger favor 0.11, 0.25
D) 0.390
high moderate low table with #'s 0.12, 0.25, 0.05: find the probability a person of moderate risk is selected
D) 0.73
cookie shop, oatmeal, chocolate chip, 145, 480, 110, 65
D) 0.781
4 diff calculators containing 13 defective and 26 no defects.
D) 0.818
two cards drawn without replacement from 52 card deck. both cards are aces
D) 1/221
6-sided die rolled. rolling a number less than 3
D) 1/3
75 separate events, proability
D) 1/75
ten cars can park in ten parking spaces. in how many ways can they park if only one car is allowed per space?
D) 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2
how many ways can a student work 7/10 questions on exam
D) 120 ways
jeff, karen, lyle, maria, norm, olivia, paul: in how many ways can the awards alternate between men and women with the first award being presented to a man?
D) 144
jeff, karen, lyle, maria, norm, olivia, paul: in how many ways can the awards be presented so that Maria and Olivia will b next to each other
D) 1440
machine produces bolts with .30 inch diameter and .01 deviation, diameter greater than .32
D) 2%
urn contains four white balls and three red balls. balls are drawn from the urn, one at a time without replacement, until two white balls have been drawn.
D) 2,3,4,5
how many 5-digit numbers can be found 1-7 if repetitions are not allowed
D) 2520 five-digit numbers
license place consist of two letters followed by 4 digits: at least one letter or digit repeated
D) 3,484,000 licenses
license place consist of two letters followed by 4 digits: at lest one letter or digit repeated
D) 3,484,000 licenses
33% of motor works are female. 70% of workers at city bank are female.
D) 32%
license plate consist of 2 letter, 4 digits. need at least one letter or digit repeated
D) 3484000 licenses
basketball player hits 45%. takes four shots, prbability hits all four?
D) 4.1%
a shirt company has 4 designs that can be made with short or long sleeves. there are 5 color patterns available.
D) 40 types
coin is biased to show 36% heads and 64% tails. coin is otssed twice.
D) 46.08%
2598960 diff 5 card-hands: all four queens
D) 48 hands
how many ways can a hand of 5 cards be dealt from 52 card deck?
D) 52! / 5!
test composed of 4 mc problems and 8 questions of T and F. each multiple choic problem has 4 choices
D) 65,536
find percent between z=-2.49 and z=1.19
D) 87.7%
the set of A (u) A´
D) U
company a and b advertising campaign. (1.0, -.6) 2x2 matrix
D) company a should use tv with 5/13 and 8/13
joe and amy two slips of paper. find optimum strategy
D) joe: 7/12, 2: 5/12; amy: 7/12, 2; 5/12; value = -1/12
A´ (n) B is the set
D) male professors under 40 years of age
male, 342, 424, female, 324, 102, total, 666, 526: student is female and ed degree not received
D) p (f l e') = 117/373
bag containing 6 red marbles and 9 green marbles. anne picks 3 marbles
D) p = 3/5, n = 3
male, 342, 424, female, 324, 102, total, 666, 526: student is male
D) p(m) = 724/1009
george drinks milk or he eats chocolate candy bars
D) valid--disjunctive syllogism
p(a) = 0.4, p(b) = 0.6, p(aub) = 0.75: find p(a n b')
E
p(a) = 0.4, p(b) = 0.6, p(aub) = 0.75: find p(a' u b')
E
p(a) = 0.4, p(b) = 0.6, p(aub) = 0.75: find p(a' u b)
E
p(a) = 0.4, p(b) = 0.6, p(aub) = 0.75: find p(a' n b')
E)
500 coins are tossed: exactly 250 heads
E) none of the above
T/F permutation: 5 delegates chosen from 27 students to bring petition
False
T/F permutation: a blend of 3 spices taken from 6 spices on a spice rack
False
T/F permutation: a sample of 10 items taken from 69 items on an assembly line
False
a coin is tossed three times, eight equally likely outcomes possible: A and B independent events
No
being dealt a card from standard deck. will the probabiltiy that you are dealt a king still be 1/13
No
strictly determined matrix: -1 , 8 (4x2)
No
strictly determined matrix: 2, 0 , -1
No
(0,4,-7) 3x3 matrix
R: 0, 9/11, 2/11 C: 0, 1/11, 10/11
(2,3,-2) 2x3 matrix
R: 1/3,2/3 C: 1/6,0,5/6
p and q
TFFF
if p, then q
TFTT
p or q
TTTF
T/F permutation: arrangement of 18 people for a picture
True
T/F permutation: batting order for 9 years players baseball
True
T/F permutation: selection of chairman and secretary from committee of 19 people
True
8% left handed, 53% female, 4.24% both female and left handed.
Yes
strictly determined matrix: -1, 0 , 3 (3x3)
Yes
strictly determined matrix: -2 , 4 (2x2)
Yes
me: drawing a spade from deck and drawing an ace
no
republican democrat , favor oppose, stronger gun control, 0.08, 0.22
no
if u = q,r,s,t,u,v,w,x,y,z; a = q, s, u, w, x, y, z; c = v, w, x, y, z, (A (u) B)´
r,t,v,c
a group of 25 ppl w 10 brunettes, 8 blondes, and 7 red head. 20 girls w 8 brunettes, 7 blondes, 6 red heads
yes
event the card is a club or three. a and b independent?
yes
me: being a teen and being a us senator
yes
