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Unformatted text preview: MATH 110 EXAM 3A DECEMBER 3, 2003
Name ‘ Section '
SHOW ALL WORK! K >/
[9] 1. An experiment consists of a player rolling one sixsided die and spinning one
wheel and recording what is marked upon them. The wheel is divided into
three equal segments marked with A,B or C respectively, on its segments.
(a) List the elements in the sample space, S, of this experiment.
, 5:. [Ah AZ, A3, A9, 43, AC», 3&3.
Bl; iii, [53, (3&1, 33, Bio,
Ci, (“2, C3, Cq} cs, C(p (~\ (2* 3V: Memkk)
(b) List the elements in the event E, the number rolled is less than 3 and
the wheel stopped on a vowel.
E = E A i, AL: 39%.
{.4 Pi. it: A z; indoclmt. 3
(c) Find the probability that the wheel stopped on B.
(a t,
/l t “/3 5"“
[9] 2. Let A and B be mutually exclusive events with P(A) = ~§~ and P(B) = Find the following:
(6) HM : \ —?(A) Zp‘ls
1 l " Z/3> : \/3 \Pt.
(b) P(AUB) 1 WA) + we) ~ P(AOB) no; ﬂammzo \
: Z/S * V‘t — o Sipir K \‘ﬁ' : “AZ '7’  q i 7’
(0) PM I B) ' '
: P(A  :O
we) om (PK/Ans) =0 , (A)
\ /‘—V‘”\_J \/»~ 1  / pi , P
[8] 3. Let S beasample space and A and B events.
T® (a) P(AUB) = P(A) P(B) if A and B are inde '
pendent. 9 CM.
ﬁT® (b) If P(A) = P(B) then A and B are complements. ZPk a
CDE (c) P(S’) = 0 . (d) If A and B are independent, then AnB = Q) 4. A die is weighted in such a way that 2,4 and 5 are twice as likely to come
up as 1, and 3 and 6 are four times as likely to come as 1. [7] (a) Find the probability distribution.
x = P(\) M J 2x = Hz) = P(‘i)=l>($)
Foch
{Lix =v Pia) = We) 21* X+Zx Mix +0.41% +Lix= \ my iSX :\ x :1 \/,5
[3] (b) What is the probability of rolling an even number?
i>(2)+ We) +Wlo) = 2.— t 3.43, _._. g
T '5 is )5
\/‘/.M—~ WNW/WW .............. My} Wﬂwemw—MMWMMJ
Zp'is V  I Pt . 5. The probability that Sean buys a new car and vacations in Hawaii is .05.
The probability that Sean vacations in' HaWaii is‘”.'15. The probability that
he buys a new car is .10.
[4] (a) What is the probability that Sean buys a new car or vacations in
Hawaii (or both)?
V : Vacsh2va / C ‘6 Mm) can" WUC) = PM + WC) ~— PKvnc) Zpﬁ
1‘: o + .  . o S ‘ '5' . Z ‘ P¥
[4] (b) What is the probability that Sean vacations in Hawaii, given that
he buys a new car?
inc) = Pomg) 2‘96
PCc )
'3' 59.2 x i'
IO 7,: Zpts . . _
[4] (c) Are the events "buys a new car” and "vacations in Hawaii” independent
(SHOW COMPUTATIONS)?
W I MW W 1
PM . PCC) e, PHI/\Q) ipt, pwm) PW)
(°‘$) (do) '05 v‘/2_ i: .lS
N0 "' de F4ﬂden+ No , c'eP'nden+ [10] 6. If 85% of all tulip bulbs that are planted do in fact bloom and 75% of all tulip
bulbs are planted and bloom, what percentage of tulip bulbs are planted? A’: F\0W\\fd./ B: \o\O€>W\ RNA) 5' WEOA): 3 ZP.\_
:. PcA
aﬁ' g ];((B‘A) ’8S . .95: :1;
Win Z BnA) .45 P(A) E apt.
’ WA) # ,‘38 [6] 7. Calculate the expected value of X for the given probability distribution: ’ipiv E(X)= (‘5)(1)+(~l)(?>)"t(0)(.l) Hay» +(S)(.z) +(lo)(0) ' :0 Part II: For each of the following problems state the formula needed to solve the
problem and identify the value of each known variable. Then find the answer to the question. A typical answer might be:
FV = 20,000(1+.07/12)"8 = $26,441.08. [6] 8. How much would you have to pay for a 6year bond earning 4.3% simple
interest whose future value is $2500? be f
Y‘s—.0q3 Fae/i4
Fv= ZSOO
Ev: W(l+~r¥) 2th
1500 = W ( \+ (0433(0)) i la,
'P\I=1fl‘18?.28 ) [6] 9. A 7year bond cost $3500 and will pay a total of $1274 interest over its
lifetime. What is its annual simple interest rate? ‘ £53" ”" W: 3500 LPBr each
lN'l“ YUM
NT: W rt: ZP’“
lZZlLl= 3500 H?)
r = 0.057. “' P"
= 5.1% rnam )hx __ r ml reﬂu = + "1 [NT = PVn FV = PV(1 +21) W = PV(1+ 7i? [8] 10. What is the future value of an $8000 investment paying 3.7% per year,
compounded monthly, after 10 years? W =» 8000 r: .037 m: ‘2‘ Pad/x.
% ' lO FV: Mus)“ f zpi 38000 (H 03? 'Z"°
I2. “H 535.25? a [10] 11. During a prolonged recession, property values on Long Island depreciated by
2% every 6 months. If my house cost $200,000 originally, how much was it
worth 5 years later? 3plr. gym °7~ (H Fwwom) i eat
Fr 2  ' " 
t“ (.OL)L2) . 1200000 < \ #002015
m z 2" Zp\z
lPi. PV: 2,00 000 ’3 W3LH‘+.SL9
(’6th JV : 5
[6] 12. What is the effective annual interest rate of an account paying 5% annually,
compounded weekly?
im ~ 51 \Pt.
m
revs: (\+ E“... —\ zpi.
m
z 51
( \ + “£2 —\ .
7. ﬂ 7, Pt.
'  O Si Z. = 5,12 % HONOR PLEDGE: I pledge on my honor that l have not given or received any unauthorized
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 Probability theory, Pledge, new car, Tulip mania

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