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practice midterm 1

practice midterm 1 - MATH 30(Spring 2007 Lecture 1...

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Unformatted text preview: MATH 30 (Spring 2007,, Lecture 1) Instructor: Roberto Sehonznann hxfEidterm Exam Last Name: First and Middle Names: Signature: UCLA id numbes (if you are an extension student, say so): Circle the discussion section in Which you are enrolled: 1A (T 9, Matthew Keegan) EB (R 9; Matthew Keegan) 1C (T 9P Yan Wang) 1D (R 9, Yan Wang) 13 (T .97 Chfistopher McKiniay) 1F {R 91 Christopher MoKiniay) Using a pen, provide the information asked above, and also write your name on the top of each page of this exam. When the instructions to a question ask you to explain your answer, you should show your work and explain what you are doing carefully; this is then more important than just finding the right answer. You can use the blank pages at the end of the exam as scratch paper or if you need space to finish the solution to a question. Please7 make dear What your solution and answer to each prohiem is. When you continue on another page indicate this clearly You are not allowed to sit close to students with when: you have studied for this exam, or to your friends. Good Luck ! | Score i) (10 paints) in a. group of studentss 8 are freshmen, :3 are sophemeresE 3 are juniors and {5 are seniors. in how mauy waye can the students in this greup form a waiting line, if ail seniors sheuid be ahead of all juniors) ah juniors shouid be ahead of ail sophomore-S; and ail sophomore shouid be ahead of ali freshmen? need to compute factoriais, powers, permutations and combinations.) (No explanation needed, just the enswer is enough.) 2) (10 points) ROM 21 die 2 times. W $121.3 is {the conditional pro‘nabifity that the sum of the faces shown is 6, given tha‘c both faces shown are even num— bers? (Give answer a fraction or in {186211131} form.) (Explain your answer calrefuléy. ) f «9w WWW my” W‘ : 3) (10 points) A greup {if peopie has 5 adults ‘dfld 9 children. From this group: 6 peopie are selecied at random. Compute the probability that at least. one adult is select-ed. (No need to compute faetoriaia pew-31‘s1 permutations and (zombineiiensj o expienation needed, just. the answer is enough) EMM' 4) (16 points) Yam .are (£62111: two cards from a standard deck of 52 cards. Consider the events A that the two cards are spadesi and B that. ’ahe two cards are aces. Are the events A and 8 independent? (Explain your answer carefuliy.) #5 3 «mm ’ Kyr- W/W' sac-m. Mmng .5) {10 points) A screening test for at disease shows a false positive with probabiiity 1% and a. {arise negative with probebiiity 2%. In the population 19% of people have that disease. Given that someene tested positive for the disease what is the probability that he / she has the (Eisease? (Provide a Immeriea} aeswer in decimal form, or as a. percentage.) (Expiain yeur answer carefully.) , r?” gm kg: 2:3? if e a . nmwmfimmfg 6) (18 points) A box contains a. fair coin and a. coin with two tails. One coin is sebatsd at ranéom from this box and flipped two times. Let X be the ranéoz'n variable that: gives the. number of heads in the two flips 0E The coin. Find the pmbability mass function of X. {the values that you compute should be expz‘esseé &5 fractions, or in decimal form.) (Explain your answer carefuiiy.) ...
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