Midterm 2 2000 - E i Math 210 ‘ Thursday MID—TERM EXAM...

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Unformatted text preview: E i Math 210 ‘ Thursday, October 26, 2000 MID—TERM EXAM ' Name (please print): TA’s Name (please print): 0 No calculators allowed. 0 Show all work. The grader must be able to follow your reasoning. a Cross out or erase all incorrect statements that you do not want counted against you. 0 In each problem involving C(n, 7") or P(n,7~) write out one of those symbols which occur in terms of factorials. 0 Each Problem worth 20 points. mam ’FALL 2.000 7-— WAtNeER (A, Math 210 4 Page 2 1. Ten balls are numbered 1 through 10. Balls 1, 2, 3, 4, 5 and 6 are red, and balls 7, 8, 9, 10 are blue. One ball is picked. The probabilities of the various balls being the one picked are as follows: W )= — Pr<2> = Pro: e, Pr(4) = e PPr(5)= @— Pr(6) :0 Pr(7):%3 Pr(8) = %, Pr(9) = 16, Pr(10) - 1—36 Let E be the event that the ball picked has an even number. Let R be the event that the ball picked is red. Find Pr(R 1 E). it s. g .3: ‘3 burr/naval": Math 210 Page 3 2. A 13-card poker hand is dealt. What is the probability the hand contains at least 7 spades and at least 5 heart ? » - to be formed. S Assume each lB—eard hand IS equally likely g t ; \ § 2 a , fl é i S AmmummumwwmmimwmmmmaMm-wam Dummy”‘Wh‘hmifiwwhu‘wmulnflunflv Meth 210 Page 4 3. An unfair coin with Pr(Head) = g- is flipped until either 2 consecutive heads appear or a total of 4 flips has been made. Let E be the event of at least 2 heads. Find Pr(E). Math 210 - Page 5 4. An urn contains 7 red balls and 5 green balls. Three balls are drawn from the urn. $8.00 is won for each green ball drawn and $4.00 is lost for each red ball drawn. Assume each collection of 3 balls is equally likely to 'be drawn. Let X be the random variable describing the amount of money won or lost. (a) Find the probability density function of X as a table. Mmmmmawwm '1: (b) Find the expected value of X. Math 210 , . Page6 5. Let X be a normal random variable with mean or expected value 8 and standard deviation 10. Find ' (a) Pr (X 2 20) (b) PI (12 < X < 18) (C) Pr (03X 3 15) ...
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