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Unformatted text preview: NAME 4 U “7/0 lie/c5. Exam 1 Grade:
ACSC/MATH 347/447 Exam #1 100 Points Total March 4, 2010 course Average: You must show enough work, or give sufﬁcient explanation, in each problem to clearly indicate how
you obtain your answer. No credit will be given for a problem if there is insufﬁcient work/explanation. You may leave binomial coefﬁcients and indicated sums and products in your answers unless otherwise
directed in a problem. 1. (12=4+3 points) A student wishes to arrange 5 different history books, 3 different math books, and
4 different novels in a row on a shelf. a. In how many ways can she arrange the books? ear/m, w 1;; Jae/945*,»
#‘ [,5':‘P{IAJIQL) 1:515: i b. In how many ways canshe arrange the books if the books of each type must be together?
50‘ ritual/2’5: (:3 l ) ~ (54 M3!” H) 2. (6 points) In how many ways can a child arrange 5 identical red blocks, 3 identical blue blocks
and 6 identical green blocks in a row? 77% W ﬂea a; 3 767/224) 3. (6 points) A club with 50 members is going to form two committees, one with 8 members and one
with 7 members. In how many ways can this be done if no person can be on both committees? 4. (18 points) If Y is a random variable with mean 6 and variance 7, ﬁnd: a. E(3Y—5) T: ~§ 3 3° é‘ﬁ’; 3* b. V(3Y—5) "1 V 7" 3al 2 Ci” 2 Q 3
c.E(Y2) = V('\()+LEC\H];: 7+éa: ‘7‘3 7‘ a W WU: BTW) {ED/W 5. (18=4+4+4+4+2 points) Let A and B be any two events in a sample space, S, such that
P(A) = 0.4, P(B) = 0.5, and HA 0 B) = 0.1. The experiment whose sample space is S is performed. a. Find the probability that the event A did not occur. PM): 1.2 PM) : 1—0.9 caé W. b. Find the probability that either event A occurred or event B occurred. FiﬁVB) :.P(.'4')'_FP(.B) "PDQ/H3)
: 06.7, +004; ' (:2. J.
:1 c. Find the probability that event B occurred but event A did not occur. 5 d. If the event B occurred, ﬁnd the probability that eventA also occurred. .» 9" / " a .
PDQ/“3): W 1:93.]? :. 1L. :0
‘ PUB) a5 5 e. Are events A and B independent? You must give a valid reason.‘ a 2, W P(AIB):0°1=F0cEf 2PM) a; 3M. PM) PCB) : (22.4)[0a55 : 0a a
i 001 =Pm/m) ’— 6. (12 points) A biased coin, twice as likely to come up heads as tails, is tossed once. If it shows head:
a chip is drawn from urn I which contains three white chips and four red chips; if it shows tails, a
chip is drawn from urn II which contains six white chips and three red chips. The coin was tossed
and a chip was drawn as described above. Completely evaluate your answers in this problem. a. What is the probability that a white chip was drawn? ‘
Z. n: .L PlH):9~P(T) 2:) 99(I4):g)i>(7> 3
H z?) law/L“; ’3' 7":5 WMJI w/BR; PM): PM) WWW) mm thm xr, 1/773
Z ﬁv.,,%\(%\)f(‘1;)(,g.) _;.£ ,7+? = 3—1
£33
a“? b. Given that a white chip was drawn, what is the probability that the coin came up tails (i.e., the
chip came from urn II)? \i 31
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3 “2.6 ‘53  ‘7 3;; '" ’6 7. (22=4+3+4+6 points) Let Y be a discrete random variable whose probability function, p01), is given
by the table below (one value is omitted). a. Find P(Y= 4). b. Find P(Yis odd I YE 2).
c. Find E(Y). d. Find the variance and the standard deviation of Y.
y 0
p01) 0.15
yp(y) C)
y2p(y) C9 (‘19 P(Y31f) : i—[yi’mrgau) +51%» +&9(3JL( = a» 1,0 (KN) P(Yoaidly‘sa) :: ﬁve/10M 2t Yam PM a at)
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give _ if"
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( ,) EU) $0???) ﬂﬂgMX 8. Eight people, four men and four women, are to be divided into four pairs to play bridge. a. (6 points) In how many ways can this be done if each pair must contain a man and a woman?
[Hintz Think of pairing each woman with a man.] b. (6 points Extra Credit) In how many ways can the four pairs be chosen if there are no gender
restrictions? [Be careful. There is no ordering to the pairs; all that matters is who plays with
whom] I: , " ' W W ) : " 75%.,qu _ “7/6,, cm, jaw i W ﬂ “1 a a L 412MHz; rxjerxszm/ <%ams Rafa/w m (y. 34/ r, \ f V 'ﬂiﬂ’m/ a tux/av
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nix ,4 :( j H A; A A ’— Q‘ 9’1 ‘7' ~31  allllzliai‘ , L I) "7‘5 ~25 if " 105:” 9. (6 points Extra Credit) Suppose that A and B are two events in a sample space, S, which are
independent and which have equal probability, p, of occurring. Suppose further that the probability that neither A nor B occurs is 0.81; that is, P(A n B) = 0.81. Find the probability that both A and B
occur. PM): We): 00
5’0 WK): P(E’)‘:l”f
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 Statistics, Probability

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