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Unformatted text preview: ‘OLUT Math351 Spring 2010 Exam 1 Part 1. Solve all problems 1 through 5. Problems 1, ‘2, 3, 4, and 6 discuss a fair die painted as follows: faces 1 and 2 are
painted in Red, faces 3, 4, and 5 are painted in Green, face 6 is painted in Blue. (1) (9 points) The painted die is rolled once. Consider the following events:
R: the die lands Red side up; E: the die lands even number up.
Determine whether R and E are independent. (Explain) P<R>= PW} —— 1% P(RE>:Pf23= 2 yes
P(E)=P{2,Ly,t}fo—:.iZ ‘;«2\=—6L\/ (“Mae/kwf (2) (9 points) The painted die is rolled once. Consider the following events:
G: the die lands Green side up; E: the die lands even number up.
Determine whether G and E are independent. (Explain , l \
p(ér):P(32L’)§5 = PCGE):P1“15 =3
pCE): é: FjJCuW (3) (9 points) The painted die is rolled 12 times. What is the probability that it
lands Red side up exactly 5 times?l (£3) em)” «see (4) (9 points) The painted die is rolled 12 times. What is the probability that it
lands Red side up exactly 5 times and Green side up exactly 4 times? 5” 8 7
222,3 (5) ever: ( <:> Gr) (5) (9 points) Given that: 0 Events A and B are. mutually exclusive:
I A and B are independent;
o PM) = 0.65, ﬁnd P(B). (Explain) A). P( : A15) : P(¢5) : O
Slum, O ) P(B)=O l1n Problems 3 and 4, it is enough if you write the formula invulving. for example. factorials
or binomial coefﬁcients; do not ﬁnish calculations. Part 2. Solve two problems of your choice from the three problems 6, 7, 8. There
is no extra credit for solving all three problems. Please do not forget to indicate which problem you decided to skip.
(6) (15 points) The painted die is rolled until it lands either a Green or a. Blue side up (then the experiment is ﬁnished). What is the probability of the event that the
experiment ﬁnishes with the die landing Blue side up?2 ppm :P{%)RB)RRB)RERBJ....} = carelm 3
—_L Li. ERA. z i
“‘ e “l e‘tllé) g, *(Z)‘g*~~
.i .L ‘
._ £2  235’ ,,_r— l"'}{ 2/ 2Conﬁrm your answer with an argument; you will not receive F1'11 :redit for only giving the r answer in the form. for example 2:6. without. explanation. (7) (15 points) An urn contains 5 Red balls, 4 Green balls and 1 Blue ball. Balls
are taken from the urn one by one without replacement. What; is the probability that all Red balls come out before all‘ balls?
Efrem“ _ r M5) LR S+Lf+
bewkce (Rdg'ﬂi‘xm 5 .. .
wag5 We gel/F.9d! W l 5
5‘ . L1}.  \O ._ “L.
/ ' I ' q
\o‘. q. (5.) (8) ( points) An urn contains 1 Red ball
ball. onsider the following events: R0: the Red ball comes out before the Green ball;
R2: the Red ball comes out the second. Calculate the following probabilities:
13090) = [/1 (gear sxmne'ﬁvl 3W6 {S G... 41 CorVebpeﬁJ‘Ace
PWGIRE): 64‘wa“ «£6 Okl‘CWS Wheh E W3") .
Kean/re C?!wa Ctva ‘Uu. 3e Wk” )
am no? “£50 exilve ~\o Va 62 6:54ij
W OWCoﬂ«ls WW R Gen/mes W £64011 6' ) , 1 Green ball, 1 Blue ball and 1 Yellow ...
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This note was uploaded on 10/27/2010 for the course MATH 351 taught by Professor Moumen,f during the Spring '08 term at George Mason.
 Spring '08
 Moumen,F

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