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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 sophomoreS; 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
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my”
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: 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 selected. (No need to compute faetoriaia pew31‘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
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Kyr
W/W' sacm. 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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 Spring '07
 SCHONMANN

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