pracexam3sol 17C

pracexam3sol 17C - Math 17C (Spring 2007) Kouba Exam 3 Your...

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Unformatted text preview: Math 17C (Spring 2007) Kouba Exam 3 Your Exam ID Number __________ __ 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO. 2. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENT’S EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION. 3. No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM. 4. Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will NOT receive full credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important. 5. Make sure that you have 7 pages, including the cover page. 6. You will be graded on proper use of limit, derivative, and integral notation. 7. You have until 9:52 a.m. sharp to finish the exam. 1.) Let sample space (2 = {0, b, c, d, e, f, g, h} with all outcomes equally likely . Let events A = {a,b,c,d}, B = {c,d,e, f}, and C = {e,f,g,h}. a.) (6 pts.) LIST the elements in sets A U B, B F] C, and Ac . Aug: ga/bJ £205 6/41}, 8/] Q: lefl‘C3/ AC: Ea/‘Fjgj b.) (4 pts.) Determine the probabilities P(A) and P(B) . P(A): ~§~‘—: ~31, 9(6): -§—-=—,‘z c.) (4 pts.) Determine the probabilities P(A n C) and P(A U C) . A/lC:;5—a (0(A/1C):o ) AUQ:A --‘r PCAUQ)ZL 2.) (9 pts) Assume the probability that a newborn is a boy is exactly 1/2 and the prob- ability it’s a girl is exactly 1 / 2. If gender outcomes from child to child are independent, what is the probability that a family of 6 children will consist a.) ofall girls? P(GGflG/G—G): (#0,: Kg? b.) of4 boys and 2 girls ? 0(‘(8l5/ 3 461i); c.)atleast1girl? P(oewiw) : (N WWW) :1“ (3003's): (~(%)“°: z— 2‘; z 5.3 3.) (8 pts) A group of 15 pe0ple includes 8 men and 7 women. What is the probability that a committee of 6 people chosen randomly will have exactly 4 women and 2 men? <23“) " WC‘iW/‘Z’VO: 0,1755 4.) (12 pts) (Genetics~ Mendel’s First Law) Gregor Mendel (Austria 1856) studied pea plants and the color of their flowers determined by two genes in their chromosomes. Assume that the following genotypes are possible : CC, Cc (same as CO), and cc, where types CC and Cc produce RED flowers and type cc produces WHITE flowers. Suppose that you have a batch of red- and white-flowering pea plants, where all three genotypes CC, Cc, and cc are represented. Assume that 25% of the plants are type CC, 35% of the plants are type Cc, and 40% of the plants are type cc. You will pick 1 parent plant at random from the batch and cross it with a pea plant of genotype cc. What is the probability that the offspring will have RED flowers ? ' ‘0»qu PW - .412 273 10° [00 35’ (06 _’:L 4 44 :7 cm, Q/q, (whl‘he) (wed (so {00 400 .L(OO ‘00 :29— “; (‘70 3; 0 4A 90%)) : 400 47 “0° “00 f 5.) (12 pts.) Play the following game with your roommate. You roll a fair six-sided die one time. If you roll a 1 or 5 you win 75 cents from your roommate. Otherwise you lose 30 cents to your roommate. What is your expected monetary outcome ? PCXL‘X) 4€E¢ it 56K): 751%?)‘ 3°Cié/ -304: q/(p :@-L’33:_33:6’5£ 6 6 G 6.) (12 pts.) A blood test for the HIV virus shows a positive (+) result in 95% of all cases when the virus is actually present in an individual and in 8% of all cases when the virus is NOT present in an individual (false positive). Assume that 15 out of every 100 people are carriers of the virus. If a person tests positive (+) for HIV, what is the probability that this person IS a carrier of the HIV virus ? W MW r 8 15 F551; \,0 F/ loo Cf) c-i er} 0’) was “75' “0 7&0 10/000 (Globe 10/000 10/000 802-. WAAMW) "3 87°“ PM HEM) = : ’X. 0- 4’77 (isles; (7256’; 7.) (12 pts.) Consider a bag With 10 red and 15 white baseballs. Randomly select 1 ball. REPLACE it. Do this 20 times. Let random variable X be the number of red balls selected. __ {o 2 3 . ~ 0 _ 2 ~— ~. ~ _ V“ ’2 / P l * a.) What is P(X = 6) ? 0‘75. 51/ 5— w, were)“ 2 o. b.) Determine the expected value ,u = E (X ) . /u\ : mp : 20 <3: : 5’ 5 0.) Determine the standard deviation of X . VQV‘ (X) : 1fllo<"/Oj 3 020(%/('53= : 4,8 —> Sam—.- 1/43' x 0?. 1‘7 8.) (9 pts.) Toss a fair six-sided die twice. Let A be the event that the 1st toss is an even number. Let B be the event that the sum of the two tosses is 7. Determine if A and B are independent events. A: (M toad A/Q/O/ICO D 6): AW 44 “7-. 6/119 52/75: <45; 34 A/m): Eagqgm}. fl/l/LM 3ézé-C M J 9.) (12 pts.) Consider a sample space Q of people made up of 400 men and 600 women. Define discrete random variables X : Q —-’ R and Y : Q —» R by A _ 0, if a: is male (M) X”) — { 1, if a: is female (F) and my) = { 0, if y sleeps less than 6 hours each night (NS) 1, if y sleeps 6 or more hours each night (S) The frequency of results are represented in the following table of values. Convert this information into a joint probability table. (n) (F) >94) )9) =0 : 1 (NS) Y=o 250 (S) Y=I What is the probability that a person selected at random is a.)afemale? lobe—4):.— o.qo+ 0.40 : 0.6» b.) a male who sleeps less than 6 hours each night ? pcxzoj \/:0) Z; O. 016/ c.) a female or sleeps 6 or more hours each night ? POW 0R Yd) = P<><=I/+ MW)» POM/w) : <0.‘40+O.20 + (o.l€+%6) _ CW) : 0.76“ The following EXTRA CREDIT PROBLEM is worth 10 points. This problem is OP- TIONAL. 1.) Assume there are 365 days in a year. In a group of 25 people, what is the probability that at least two people have the same birthday (same month and day) 7 pQwW 1W): 1» WWW) 3g5.3699343~‘ 34! :i—r 3e52y BQSRS’ 2: 0. 5687 ...
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This note was uploaded on 11/26/2010 for the course MAT MAT 17C taught by Professor Kouba during the Spring '09 term at UC Davis.

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pracexam3sol 17C - Math 17C (Spring 2007) Kouba Exam 3 Your...

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