econ_41_midterm_review

econ_41_midterm_review - ECON 41 Section 1B Review Session...

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ECON 41 Section 1B Review Session for Midterm Oct. 30, 2006 Hisayuki Yoshimoto 1 Last Update: Oct 28 1pm 1 Chapter 4 Questions Exercise 4.125 (Textbook P.178) In a class of 35 students, 13 are seniors, 9 are juniors, 8 are sophomores, and 5 are freshmen. If one student is selected at random from this class, what is the probability that this student is (a) a junior (b) a freshman (Answer) P ( Junior ) = 9 35 = : 2571 P ( Freshman ) = 5 35 = 1 7 = : 1429 : Exercise 4.133 (Textbook P.180) Refer to Exercise 4.125. Two students are selected at random from this class of 35 students. Find the probability that (Answer) P ( 1st Junior and 2nd Senior ) = P ( 1st Junior ) P ( 2nd Sophomore j 1st Junior ) Notice that (1st Junior) and (2nd Sophomore) are not independent = 9 35 8 34 = : 0605 : Notice that a second student is selected among 34 (not 35) students. Exercise 4.134 (Textbook P.180) A company has installed a generator to back up the power in case there is a power failure. The probability that there will be a power failure during a snowstorm is : 30 . The probability that the generator will stop working during a snowstorm is : 09 : What is the probability that during a snowstorm the company will lose both sources of power? (Answer) P ( Losing both sources of power ) = P ( Power failure ) P ( Generator stops ) Notice that (Power failure) and (Generator stops) are independent. = ( : 30) ( : 09) = : 027 : Exercise 4.145 (Textbook P.181) A gambler has given you two jars and 20 marbles. Of these 20 marbles, ten are red and ten are green. You must put all 20 marbles in these two jars in such a way that each jar must have at least one marble in it. Then a friend of yours, who is blindfolded, will select one of the two jars at random and then will randomly select a marble from this jar. If the selected marble is red, you and your friend win $100 : red marble? (Answer) 1 [email protected] My o¢ ce hours is Wednesday 9:00-11:00am. Students are encouraged to ask questions in my sessions. 1
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There are 2 jars. I name them jar 1 and jar 2. For notation simplicity, use the following noteations J1 = Jar 1 is selected by your friend J2 = Jar 2 is selected by your friend R = Red marble is selected G = Green Marble is selected P ( J1 ) = 1 2 P ( J2 ) = 1 2 : In question (a), we have Jar 1: 5 reds and 5 greens, totally 10 marbles Jar 2: 5 reds and 5 greens, totally 10 marbles : Next, when your friend selected a red marble, that red marble came from either jar A or jar B. Events "A selected red marble comes from jar 1" and "A selected red marble comes from jar 2" are mutually exclusive, because it is impossible
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This note was uploaded on 10/14/2009 for the course ECON 41 taught by Professor Guggenberger during the Fall '07 term at UCLA.

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econ_41_midterm_review - ECON 41 Section 1B Review Session...

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