MA206 WPR 1 - Sheet 2 Cadet V[MA206 AY15—01 Version 1...

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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 LO PCAnmgfl mow : .\ )— .H-nl .. .55 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! 01-144 inSLQW')’ Lvtcuu 5L ¥= P ® Sheet 3 [MA206 AY15-01, 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 ’ A. V 3 ‘ vans-J“ 30" a ' c), Points] When you initially selected the three aircraft, what is the probability that ' A you selected AEELEAgT" 6N E working aircraft? l 7 YL mm. Tot-A 4., , r / b '15 finc¥wm\ 9" 1; O\ / , 7 N pmhab:t;i»\ A“ WOW" 5" M ‘ 1—0.01‘63 a. it has" 1 N _ 3 0.0V“? 5 ' a) [10 Points] Define Sheet 4 Cadet [MA206 AY15-01, 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 . ‘5 .q A '9 :fl‘rMu‘)‘: pog‘h’u, 8—» 415*! [3094»— ?40‘3) A‘A Ad'wv’g‘" ntjov‘wc 3 ‘4 rest (“Tam 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 I/ 1 V (Army? 9mm) - 9043- 9(3) comm» : [0.006% ] [MA206 AYl5-01, 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‘scfiwS-Fm as omuswl ‘0 0‘“ accurate Dem“. fake “posihw. ', 25 MN, HRH} Sheet 6 [MA206 AY15-01, 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 sub-network 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 . ' , I I 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 sssés, 55?; r=\=,,, €56 W I V st 55} iii: 5! 55, I 66 ALF—5% ‘ L“ We W .x, 7, lam ffiww L ' 6 F Sheet 7 4 [MA206 AY15—01, Version 1] 8 September. 2014 ' 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 AY15-01, 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, ‘2 LLML (YA) -, 75 \‘3 Afith N bud“ '5 %A&\ 3 :1. (“RA d’ “with at NHLI, N PCAIwy PCAAw) c (ma 6 ‘ W, > v» . 0cm 7 N ' N1 ,_ \ C 7- - 2104-23! 4‘“, . g:- E Jr ISLE—w _ _ r ‘p :44?- lf' a. “*2. 00592;“ __; 2+ M) (grub! fig,» _ . \ ; IL com as I '3. Z: GAN‘JI‘A‘. _ 1",. , N»: Q N 77: ($1, ...
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