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Name Section Math 110,Exam 3A May 3,2004
Show all work! [8] 1. Let P(A) = .35 and P(B) = .45. If A and B are mutually exclusive events, ﬁnd the following. a) P(AUB) b) P(AnB)
219(A)+P(5) ﬁll :0 —~_; 4’
= (7.35 rosy : ——~—> 2i [9] 2. A game consists of a player rolling one 4sided die and drawing one card from a stack of 6 cards.
The die has the numbers 1,2,3,or 4 respectively on its faces while the cards are printed with the letters
A,B,C,D,E,or F respectively. a) Write a sample space of equally likely events that includes all possible outcomes for one player’s
turn at the game. §={1Ar1/‘\,3AI4A1’5/15/35,+B,/C,3 c,3c,+c / 10,20,311“), IE,ZE,SE,+E,IF, 2.5.x, 4F
3 l
b) List the elements in the event M, that the player rolls an even number and draws a consonant.
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/:> 3 M={2v3,2c, 21111:, 4B,?C,4D,4Fl c) Find the probability of rolling an odd number, given that you roll a number less than 4. pacing a mutt/m1 W4) = Paola: (at at; z #4)
{’(nu a a <4) 2 ¢3_
:lvj
4‘, [16 3. Circle the correct answer
T a)Given sample space S ={x,y,z}, then P(x)=.7, P(y)=.3 and P(z)=.4, is a valid probability assignment.
@ F (b) If there is a 60% chance of rain today, then there is a 40% that it will not rain today.
T c) The conditional probability of E given F is P(E l F) = P(EuF)/P(F).
d) The probability that Susan will play the lottery and win is equal to the probability that Susan
will win given that she played.
T F (e) If the event E is impossible, then P(E) = 0.
T’®(t) Events A and B are independent if P(AUB)=P(A) + P(B).
F (g) When interest is compounded, interest is paid on previously earned interest.
(h) Investing at 8%, compounded quarterly, is better than investing at 8% simple interest. ‘ I (12) 4. A realtor has 12 houses to sell. During a given week, 4 of the houses are advertise elevision,
6 on thenzadio, and 2 on both radio and television.
a) Find the probability that a randomly selected house is advertised on radio. £4. “sag {1‘1 b) Find the probability that a randomly selected house is advertised on the radio or television (or both). New): Pow P/r)~ wen r) a”) 2' ‘ A f i K i T. ﬁlm/(yon
‘ {1 p’ ‘1 _ R: RAUL)
\ j z 3. > 2
“ 1.1 5
0) Are the events “advertised on the radio” and “advertised on television” independent?
(SHOW COMPUTATIONS.)
Poemﬁi’ié x _ /72
16. iaLL j§P(pnr)‘P(k)Pcr)
WW)“ (2 o. v.5 ~
AU *9 2' (8) 5. The probability that Mary will buy a new book this weekend is 30%. The probability that Mary will
wash her%ar this weekend is 60%. Assuming that Mary’s purchase of a new book is independent of her
washing her car, what is the probability that Mary will either wash her car or buy a new book (or both) this “$33203 3(7 (“éme of 8 M1 3}] *9 3)
FCc):o.(, [NMCFFW f(c)=0.5 (0.00.:
F(5UC)‘F03>+P(C)~}>(s/ic) \, 3’ 1‘0.6~0.3:0.72’\> Z, (8) 6. Of registered voters in a community, 55% are Republicans, and 30% are Republicans AND favor
building a new jail. If a registered voter is selected at random, ﬁnd the probability that the person favors building a new jail, given that they are Republican. '
PG 0 g) :93 “'91 ) P02) toss— > 1'
"/l2 03
F0 A?) = H J = "’ = 05¢; (6) 7. Calculate the expected value of X for the given probability distribution: 0v"
#9 X 5 1 0 7 9 1o P(X) .05 .2 .15 .1 .3 .2 at Luv WW ‘\ EX :(fS‘NWS'j/t (0/5] 74 my 7 9(0.j)/> 5'
Jr (0(o.2) : 4e95 __a /: 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. Calculate to the nearest cent, nearest .01 %, or round to the 4“I decimal place.
A typical answer might be: FV= 20,0000 + .07/12)48 = $26,441.08 (6) 8. $4575 was invested at 3.2% simple annual interest for 5 years. What is the future value
of this investment? \ PV'JQLI'U' { ad‘ {:0032 FVWVUT Vb) M 2’
it? 2‘ 4%? (1+ 0052(5))
FV“. =50] «M /' (6) 9. A $7500 investment earns $875 in 5 years. What is the annual rate of simple interest? Pv=7roa _”
": 2
I? 575’ 57k =75‘ovm’) 5' i \(37 Y:0\025:g.)77 _.._> /, 1' each rnom m_
INT=PVrt FV=PV(1+rt) FV=PV(1+7%)"" ref/=(1+ m ) 1 (5) 10. What is the effective annual rate of an account oﬁ‘ering 025% daily interest, compounded daily? g
e°1’ (‘ 7'0 f0 ’0 6‘ yd: 2 (if :nm) “/ We? 2
Ynom:0‘owzy X 3U» j MUG}
\i’< : “0% ‘5" NZ I : 047002;)36314 >[’ (8) l 1. If $2000 is deposited in a savings account paying an annual rate of 6%, compounded
quarterly, how much will in the account at the end of 15 years? PV=2000
' Cﬂd‘l Y:0\(}(} I mlq 405)
tzls 32000 C H : 4273 6430 “Map /’ (8) 12. Inﬂation has been running at 4% per year. Grass Mulcher lawn mowers costs $625
today. What did a comparable lawn mower cost 7 years ago? YW‘U‘F _ Fl/ . 7 j’
W mm W“ MW“ m i w ma! ' (#00507
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 Probability theory, Dice, Probability space

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