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Unformatted text preview: Sheet 2
Cadet V [MA206 AY15—01, Version 1] 8'September 2014 Sectio‘n#_n~_~w WPR 1
PART I: 40 Points Your unit just receiVed two brand new MRAPs from theater supply to replace the two that
your unit lost in a VBIED strike. You’ve heard some rumors that the engines in the MRAPs
are not as good as they used to be. Let A be the event that the engine in MRAP 1 fails. , Let B be the event that the 6W. From the manufacturer’s test data,
you estimate the following probabilities: AND
PM o B’) = 0.3, Figure 1: MRAP Vehicle ' a) [10 Points] Draw a complete Venn Diagram using the given information. Make sure to
label the probabilities in all of the regions of the sample space. _ b) [10 Points] Calculate the probability that AWone of the two engines fail. {me} : ‘Pmi 9553+ PLAABB z x'lfh‘4,'l,_"3. 5: c) [10 Points] Calculate the probability EXACTLY ONE engine fails. I  * mm
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Li’oux work. (WW A“ ‘ d) [10 Points] Are the events A and B mutually exclusive, independent, or neither? For full
credit, you must provide justiﬁcation. to {\B+O A anal 6 ma; (schism; “MK A
/ Pr an! 01144 inSLQW')’ Lvtcuu 5L ¥= P ® Sheet 3 [MA206 AY1501, Version 1] 8 September 2014 Cadetw Sectio
WPR 1 I PART II: 40 Points You are assigned to the 10lst Combat Aviation Brigade as an assistant operations officer.
You immediately reSearch the capabilities of t e brigade and ﬁnd that it has (1/9): CH47
Chinooks,@9)x OH—58D Kiowa Warriors, and 6x UH—60 Blackhawks.  . '3‘; 4—.M
a) [15 Points] Your unit has been tasked to support a community air show that will require
the use of three rotary winged aircraft (the type of aircraft does not matter). Since you are
trying to be fair to each unit, you decide to randomly select aircraft to task. What is the probability that you select of each type? I5 )0 Q _ a I _ (9
L ’3') = “ﬂamio = J Q «9
L537 "7770, b) [15 Points] Your OPS sergeant gets wind of what you are trying to do and reminds you to check the NMC (Non—Mission Capable) report; He tells you that not all of the helicopters in the brigade are ready to ﬂy. You check the NMC report and ﬁnd that 4 x CH47s, 3 x
Q‘ OH—58Ds, and 5 x UH—60s are all down for repair and will not be available for tasking. If
you have already tasked one helicopter of each type, What is the probability that ALL of the
helicopters that you tasked for the air show are NMC? ‘ ~ ‘ J“ ‘ m C '3: act )6 NML (LX963 f to. 001? / cam». 34— \°  Mm m
(3'33) 7 ’7 7o
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vansJ“ 30" a ' c), Points] When you initially selected the three aircraft, what is the probability that
' A you selected AEELEAgT" 6N E working aircraft?
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Cadet [MA206 AY1501, Version 1] 8 September 2014 Section—#__ WPR '1
PART III: 40 Points You have been chosen to take part in Army experimental research to help develop a new
urinalysis teSt that improves the accuracy. You have been working with the head chemist
and ﬁnally come up with a test that correctly identiﬁes positive samples with 97% accuracy
and negative samples with 98% accuracy. Statistical analysis indicates that approximately
1% of the Army’s personnel use drugs. There are currently 400,000 Soldiers on active duty. events and draw a diagram that models the given information. 1 r .
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uO'L\ , b) [5‘Points] The Army decides to perform the new urinalysis test on every single active duty Soldier. Find the probability that the active duty Soldier uses drugs AND the urinalysis {
test is positive 1
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1 V (Army?
9mm)  9043 9(3) comm» : [0.006% ] [MA206 AYl501, Version 1] 8 September 2014 _ Section\
WPR 1 aoh‘hér anti The.» for. use ag’fmut) if) a PéSuu’ 6“ LL Clam“ 91’ A Null means 1‘—
:s a Q‘scﬁwSFm as omuswl ‘0 0‘“ accurate Dem“. fake “posihw. ', 25 MN, HRH} Sheet 6 [MA206 AY1501, Version 1] 8 September 2014 Cadet__#__n Section___._~__.. WPR 1
PART IV: 30 Points Consider the terrorist network in the ﬁgure below with ﬁve nodes. Each node’represents
a terrorist that can pass information along the network as long as he or she is alive. The
subnetwork functions if the terrorists at both nodes 4 and 5 are alive. The entire network .
' functions if there is at least one functioning path for information ﬂow between enter and
exit. Each terrorist node survives with a probability of .75 and operates independently of
all other nodes. ‘ / Enter ‘ “and—«nu. '
l I I I I I I I I I I : I I I I I I I I I I I l I I .
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In“. An experiment consists of determining the condition of all terrorist nodes where S denotes
a terrorist node that is still alive while F denotes a failed node. One outcome of this experi—
ment is SFSSS corresponding to nodes 1,3,4,5 successfully surviving and node 2 having died. a) [5 Points] List all of the outcomes that would result in a functioning terrorist network,
meaning that at least one path exists such that information can ﬂow from the entrance
through the network and out the exit. L {6%ssg
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' Cadet ' Section
WPR 1 b) [10 Points] Calculate the probability that the SUBNETWORK functions. MHMD _ (we) (75% [0.56515 5 2 ’ EX, ﬁn c) [15 Points] Calculate the probability that the terrorist network functions. Remember that the terrorist network functions as long as information can ﬂow from the entrance through at
least one path in the network and out of the exit. ' PM“ we?  \ (\[1 u (um 3 p
)\ /)\.\_N>¥\\N_ '
PM” ‘ @‘Sié‘iélr 05%“) — @313318531 (n5) : ico 5040i ﬁ—Ywmm.“ Sheet 8 ‘ ' [MA206 AY1501, Version 1] 8 September 2014 Cadet_.___ Section .. __ _ WPR 1 PART V: 5 Bonus Points \ There are two bags. Bag A contains N White balls and 2 black balls and bag B contains 2
White and N black balls. One of the two bags is selected at random (equally likely) and two
balls are drawn from it Without replacement. Given that both the balls drawn are White,
the probability that bag A was used to drawthe balls is 6/ 7. Find the value of N. l * ’ cm wkk wish,
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