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Unformatted text preview: l. (18 pts.) In 1912 the Titanic sank without enough lifeboats for the passengers and
crew. The table below looks at survival by gender. Titanic Survival by Gender 1731 2201 In working this problem, use the notation S = Survived the sinking D = did not survive the sinking (Died)
M = Male F = Female a. What proportion of the passengers survived? For fullcredit, use correct probability
notation when writing out your answer (i.e. write either P(AB) or P(A) with A, B
appropriately replaced by event(s) listed above). PO): 7/! 220 l ‘5 .323 b. What proportion of men survived the sinking of the Titanic? For/fullcredit, use correct
probability notation when writing out your answer (i.e. write either P(AB) or P(A) with
A, B appropriately replaced by event(s) listed above). 367 P(5/M)‘: 77;; 2 .217. c. Given that a passenger survived, what is the chance that they were male? For full
credit, use correct probability notation when writing out your answer (i.e. write either
P(AB) or P(A) with A, B appropriately replaced by event(s) listed above). 170115) : 317...; ,5/4
’7)» 2. (12 pts.) Keno is a lottery game. Here are the details of a Keno bet you can make in
Deadwood, South Dakota via video machine: You select 3 different numbers from 1 through 80 inclusive. There will be
20 numbers chosen as winners by the house, with the other 60 losers. Net
winnings for a $1 bet depend on how many of the 20 winning numbers you
match. In particular, here are your winnings for the Various possible numbers of matches:
Winning Numbers Net Winnings
Matched ollars v
__ 6
 7’9 and
. “gym”; a. What is the chance, in a single $1 bet, that you win $45?
( 7—D)( c. 0)
WW“ .1545) = 3 0
5’0
( 3 ) b. What is the chance, in a single $1 bet, that you lose a dollar? VZLﬂjcsl): W("7c4740 or WM I) 4: .r. = V(m.m a)* Vtmd—u‘ I)
= [3570?) + (71701")
0;") 0;") 3. (12 pts.) Multiple Choice (circle the correct response, no work is needed) a. If
P(A and B and C) = P(A)P(B)P(C) P(A and B) = P(A)P(B)
P(A and C) = P(A)P(C)
P(B and C) = P(B)P(C) then we say
' ' int events
ii. A B C are inde endent events
iii. A,B,C are complimentary events b. If each of the three pairs of events AandB,AandC, &BandC have no outcomes in common, then we say < i. A, B,C are disjoint event§ > 1i. A, B, C are independent events
iii. A,B, C are complimentary events c. P(A or B) = P(A) + P(B) is i. Always true
11. Sometimes tru 3»
iii. ‘ ever true d. P(A) = P(A  B)P(B) + P(A I B')P(B') is ' Always tru
ii. ometlmes true
iii. Never true 4. (24 pts.) A system consists of two components. The probability that the ﬁrst
component works during its design life is 0.75, the probability that at least one of the two
components does so is 0.95, and the probability that both components do so is 0.70.
(Suggestion: Let F = ﬁrst component works during its design life, S = second component
works during its design life, and draw a Venndiagram.) .05
,1 5 a. What is the probability that the second component works during its design life? P55): 320 b. Using the deﬁnition of independence, show why the two components do not work
independently. .7» = PCFMS) # PM)?!» :(.75)(.7o)
: ,575 c. What is the chance that exactly one component works (i.e. just the ﬁrst component
works or just the second component works)? mm; 59W c FM 5)) = .25 d. Given the second component works throughout its design life, what is the chance the ﬁrst one does so? 2 Lo = 1 5".73' I) :
P( F ) W5) ‘ 90 7 5. (9 pts.) A system of n components is called a k—out—ofn system provided it functions if
and only if at least k of its components function. (Example: Perhaps a roof being
supported by n beams remains intact as long as at least some number of the beams are of a threshold level of strength.) a. A noutofn system is better known as a paralleircle one) system. b. A Ioutofn system is better known asseries (circle one) system. c. Suppose that the components in a 7outof9 system work independently with chance
p = 0.75. Write, but don’t evaluate, an expression for the chance the system works. (:)Q75)"(,2g)‘ + Lyégfczy' + (3)099625)‘ 6. (12 pts.) This problem concerns the tossing of a pair of foursided (‘tetrahedra1’) dice
(each has the equallylikely numbers 1,2,3,4). a. If the pair are tossed once, what is the chance of a sum of 6? I) t : Him 6) M 5 b. What is the chance of at least one double 4 in 10 tosses of the pair of dice? FZ/M LEM a»: mag 49 r I— IVle Dauévé 7') M 127/; M M MD plum/e 5L
7 ). V(Woaaaea 4 d @479”) — /o
"‘5" [—(13 2 .1755+
lé 7. (12 pts.) In many popular board games (e.g. Trouble, Parchessi) one cannot move their
players from “home” to the general playing area until they ﬁrst throw a particular value
on the (single) die that is thrown. Suppose that a ‘6’ must be thrown, using a fair six sided die, to bring a player out. a. What is the chance that you are ﬁrst able to bring out a player from home to the general
playing area on your fourth turn? ' <97 i) b. What is the chance that it takes you at least three turns to bring out a player from home
to the general playing area? For fullcredit, give me a numeric answer. PU” W 94"”9): IIPUTVM on 2W)
Jr}.
a / ZV(/1vm)+;e(2_vunu>):2 ‘fi'"t~2’,lz 4— éﬁ] = if 8. (6 pts.) How many passwords of length 6 can be made where each character is either a
lower case letter (‘a’,’b’,...’z’) or a digit (‘0’,’1’,...,’9’)?
W m
26 Le . lo Jieib 35‘ = Lin/732,334 ...
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 Fall '04
 JOHNSON
 Statistics, Probability

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