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Unformatted text preview: MATH230
Spring 2006 Exam 1a 529 Name: Section: instructions: 1 N 0391900 . Do not start until instructed to do so. You may use a calculator and one 3x5 card (front and back) with notes,
but nothing else. . SHOW ALL WORK to receive full credit. Circle your answers. Report answers that are probabilities to 4 decimal places. . The work you turn in must be your own. 1. 6 points The route used by a certain motorist in commuting to work contains two intersections with
traffic signals. The probability that he must stop at the first signal is .4, the probability that he must
stop at the second signal is .5, and the probability that he must stop at at least one of the two signals is .6. What is the probability that he must stop at both signals?
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Proﬁt (1 8); WM) 1‘ Pr<5)— Pr [/4 U 8) :ArSlb 7W Questions 2 _ 4; Let A = {1,3,4,5} and B = {0,1,2} be subsets of U = {o,1,2,3,4,5}.
2. 3 points List the elements ofA U B.
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3. 3 points List the elements ofA m B. 3/3 4. 3 points Do A and B form a partition of U? Why or why not? N0: fr f
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A CNN] 8 a"? “0+ 3/DJ‘az/t7‘. Questions 5 — 7: You are part of a team of auditors assigned to audit the financial records of company
XYZ. The company has 20 accounts but you randomly select only 5 accounts to audit, noting how many accounts out of the 5 do not pass your inspection criteria. 5. 4 points How many possible samples are there?
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/ (120/ S) a (20's)? 3’( 6. 5 points Suppose there are in fact 2 accounts out of the 20 that would not pass your inspection.
What is the probability that you find exactly 1 account out of the 5 selected that does not pass inspection?
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O 7. 6 points Now let F = number of accounts out of the 20 that would not pass inspection. Find the
value of F that maximizes the probability of ﬁnding exactly 1 account out of the 5 selected that does
not pass inspection and support your answer. Y0ur answer is called the Maximum Likelihood
Estimate (MLE) of F, the unknown number of “bad” accounts. (You don't need to “prove” your result;
just show sufﬁcient support for it. Hint: Start with your best guess for F.) F éM'J’ [M753 20~ F 30 N“ 
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M m: m at 5 MW W? ’ 5,90% 8. 4 points An experiment consists of tossing a coin until the first head appears or until the coin is
tossed 6 times. The result of each flip (head or tail) is noted. Write down the sample space S for this experiment. What is n(S)? '— ’r ’ "‘T—Tﬂ—l
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T’TTTTT} “5):? \ 9. 6 points Suppose you are playing a board game where you move around the board by rolling fair
sixsided dice and moving the number of squares corresponding to the total number of dots face up
on the dice. At each turn you have the option to roll only 1 die or 2 dice. At some point during the
game. you can win by landing on a certain space on the board. If you are five squares away from the
winning space, how many dice should you roll? Justify your answer with probabilities. .— ’C/t
15K szl/ ZI3)L{)SICE sz/U ///’/ p Questions 10 — 11: An auto service shop has 4 service bays in a row. One morning Larry, Balki,
Jennifer, and Maryanne all bring their cars in for service and their cars are randomly assigned to service bays. 10. 4 points In how many ways can their cars be assigned to service bays? rm); l: : 2% w WWW/“W 11. 6 points What is the probability that Larry's and Jennifer’s cars end up next to each other? L'l'Z’wiw [7’
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 Spring '08
 CRISSINGER
 Probability theory, Maximum likelihood, Dice, Jennifer, Coin

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