Exam_solutions_38_A

Exam_solutions_38_A - MATH 110 EXAM 3A DECEMBER 3, 2003...

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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 six-sided 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>($) Foch {Lix =v Pia) = We) 21* X+Zx Mix +0.41% +Lix= \ my iSX :\ x :1 \/,5 [3] (b) What is the probability of rolling an even number? i>(2)+ We) +Wlo) = 2-.— t 3.43, _._. g T '5 is )5 \/‘/.M—~ WNW/WW .............. My} Wflwemw—MMWMMJ Zp'is V - I Pt . 5. The probability that Sean buys a new car and vacations in Hawaii is .05. The probability that Sean vacations in' HaWaii is‘”.'15. The probability that he buys a new car is .10. [4] (a) What is the probability that Sean buys a new car or vacations in Hawaii (or both)? V : Vacs-h2va / C ‘6 Mm) can" WUC) = PM + WC) ~— PKvnc) Zpfi 1‘: o + . - . o S ‘ '5' . Z ‘ P¥ [4] (b) What is the probability that Sean vacations in Hawaii, given that he buys a new car? inc) = Pomg) 2‘96 PCc ) '3' 59.2 x i' -IO 7-,: Zpts . . _ [4] (c) Are the events "buys a new car” and "vacations in Hawaii” independent (SHOW COMPUTATIONS)? W I MW W 1 PM . PCC) e, PHI/\Q) ipt, pwm) PW) (°‘$) (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 6-year 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 7-year 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 assistance on this examination or assignment. Please write the exact wording of the pledge, followed by your signature, in the space below: Signature~ ,, _. a ...
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Exam_solutions_38_A - MATH 110 EXAM 3A DECEMBER 3, 2003...

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