Quiz 2 Solutions - Stat 225 - Quiz 02 Name Spring 2012 You...

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Unformatted text preview: Stat 225 - Quiz 02 Name Spring 2012 You have 10 minutes to complete the problem below. Show sufficient work to receive full credit. You must work on the problem you are given: trading quiz sheets will result in a O for both parties. lfa decimal answer is not exact, please round to 4 decimal places. 1. The Patriots are playing the Giants in the Super Bowl. The Patriots have a probability of .75 of winning the game. Keep in mind there are no ties in the post—season (Donovan McNabb). If the Patriots win, they will win be at least 10 points with a probability of .7. If the Giants win, they will win by at most 9 with a probability of .9. (a) Draw a tree diagram with the appropriate probabilities filled in. (5 points) '7 l0 ma ° WM Km M m .15 F / f / WM by < [O (b) What is the probability that the game is decided by 10 or more points? (6 points) Hwy 57 :10) - Mf'wctwmmwM PM» PCmmilO‘ 6+) .7907 +2.96 ml :— . 5? (c) If the game was won by 10 or more points, what is the probability that the Patriots won? (5 points) P ) nyflwmzlo 10) "152(1'7 /_ - 4 E. O 2 W '3 W“: : bo< ‘ WM ( PCWMZlD) DST? (d) Are the events the Patriots winning and winning by at least 10 points independent? Prove your answer. (4points) SHALL 7‘" t of] 5 P(Bj)*P(A|Bj) P(AmB) P(A | B) = 13(3) II ZP(B,-)*P(AlBi) P(AC ) = 1 — P(A) P(A UB) = P(A) + P(B) —P(A n3) P(A m3) = P(B) * P(A | B) P(A) = 21303,.) * HA I B.) P<Bj IA) = Stat 225 - Quiz 02 Name Spring 2012 You have 10 minutes to complete the problem below. Show sufficient work to receive full credit. You must work on the problem you are given: trading quiz sheets will result in a O for both parties. If a decimal answer is not exact, please round to 4 decimal places. 1. Bill Polian has a tough decision for the April draft. Suppose he is going to pick a QB. He will select Andrew Luck with probability of .85 and Robert Griffin Ill (RG3) with the remaining probability. If he selects Andrew, the Colts will win a Super Bowl in the next decade with a probability of .78. However, if he selects R63, they will not win a Super Bowl in the next decade with a probability of .87. (a) Draw a tree diagram with the‘appropriate probabilities filled in. (5 points) 3/ WM 5% HS v% (10 Miami 53 (b) What is the probability the Colts win a Super Bowl in the next decade? (6 points) ‘ ' > Wm gal: HM» Maw) +HK633‘ imam”) :3 ffS xo’l‘g hlé‘ x..|3 : .6395" (c) If the Colts win a Super Bowl in the next decade, what is the probability that they drafted Andrew Luck? (5 points) é X6 f . (2)893 (d) Are the events winning a Super Bowl and drafting Andrew Luck independent? Prove your answer. (4 0,“,le O m M a. mu 56\ 7” ?(,lOl/L\"3* .85 P(Bj)*P(A|Bj) P(AnB) P(A I B) = PUB) l1 ZP(B,»)*P(A|B,-) i=1 P<A>=iP<B,—>*P<AIB.) P(B, IA)= P(AC) = 1 — P(A) P(A UB) = P(A) + P(B) — P(A n B) P(A m B) = P(B) * P(A | B) Stat 225 - Quiz 02 Name Spring 2012 You have 10 minutes to complete the problem below. Show sufficient work to receive full credit. You must work on the problem you are given: trading quiz sheets will result in a O for both parties. If a decimal answer is not exact, please round to 4 decimal places. 1. Bill Polian has a tough decision for the April draft. Suppose he is going to pick a QB. He will select Andrew Luck with probability of .91 and Robert Griffin ||| (RG3) with the remaining probability. If he selects Andrew, the Colts will win a Super Bowl in the next decade with a probability of .64. However, if he selects RG3, they will not win a Super Bowl in the next decade with a probability of .73. o q 4m (0/ wM 5B (y (’d“ 5&1 WM 56 / fl} 510 71% WM 03 m (Wd (Dy—M5 (b) What is the probability the Colts do not win a Super Bowl in the next decade? (6 point (7 140+ all any) a 9 my meal PM + H @535?lech l we) 1 Al n50 mswn‘g e .aqas (c) If the Colts do not win a Super Bowl in the next decade, what is the probability that they drafted RG3? (5 points) a {DC’é bc’ ( miles) 56‘”)? . Ofwafilb 2 @153 1 ° \ (""70 (d) Are the events not winning a Super Bowl and drafting RG3 independent? Prove your answer. (4 points) CW, mmo : fake? W59) W ¢ (Real 1 . <33 P(Bj)*P(A|Bj) ZP(Bi)*P(A|B.-) P(AC) = 1 — P(A) P(A UB) = P(A) +P(B) — P(A m3) P(A m3) = P(B) * P(A l B) Puma P(A | B) = PUB) P(A>='Z'P(B.>*P(AI B.) P(B,- IA)= Stat 225 - Quiz 02 Name Spring 2012 You have 10 minutes to complete the problem below. Show sufficient work to receive full credit. You must work on the problem you are given: trading quiz sheets will result in a 0 for both parties. Ifa decimal answer is not exact, please round to 4 decimal places. 1. The Patriots are playing the Giants in the Super Bowl. The Patriots have a probability of .8 of winning the game. Keep in mind there are no ties in the post-season (Donovan McNabb). If the Patriots win, they will win be at least 10 points with a probability of .6. lfthe Giants win, they will win by at most 9 with a probability of .75. (a) Draw a tree diagram with the appropriate probabilities filled in. (5 points) (0 > ,6 V WM 107 A [0 5B ‘/ .\ ,lo Mir W by: m ‘3 A > E e f/ “‘1‘” by ’[O (r A % WM by “(1 (b) What is the probability that the game is decided by 9 or fewer points? (6 points) me loo iq>~¢?(fl>0 Plum by EQlWJFHg/S 0 Hymn by SM 5/) i: 633% i‘ Q'Dvx Cng =- .47 (c) If the game was won by 9 or fewer points, what is the probability that the Giants won? (5 points) f, ,5 Presctéwm waded fCG—l wmloyivcw ” agefljg : aulvl (d) Are the events the Giants winning and winning by at most 9 points independent? Prove your answer. (4points) WEIR/Wk 0 WNW ll P(B,-)*P(A|B,-) P(AIB):P(AmB) P(A) = $1303..) * HA I B.) P(B,- IA) = ZP(B,)*P<A I B.) “3) P(AC) = 1— P(A) P(A u B) = P(A) + P(B) — P(A m3) P(A m3) = P(B) * P(A| B) ...
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This note was uploaded on 02/06/2012 for the course STAT 225 taught by Professor Martin during the Spring '08 term at Purdue University-West Lafayette.

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Quiz 2 Solutions - Stat 225 - Quiz 02 Name Spring 2012 You...

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