Math 112 Test

2

Name GMUID

October 19,20L3

Show all calculations in the space provided. Using a calculator is allowed (and suggestedJ, but make sure to show the calculation used in each problem. Please follow the GMU Honor Code.

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Part I (80 points) 1.. Find n(B), given thatn(A)=1,8, n(AfiB)=7, and n(AUB)=Z4.

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2. Name the shaded set

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3. In a survey of recent homebuyers it was found that ' 240 were not married . 160 were first time home buyers . Of the 325 married homebuyers, 250 had previously owned a home. How many of the people surveyed were neither first time homebuyers nor

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4. Use the Venn diagram below to find

:

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,(auclna) =

3+5+6 = I +

0t
c. n(AuB)'

:

lL+ lS

= a7

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5. Students must answer 5 out of 9 exam questions. In how many different ways can these questions be selected?

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tAG printer simultaneously.

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b) =

6. Six people in the computer lab all send documents to the In how many ways can the jobs be processed?

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7. Suppose a password consists of 5 case sensitive letters. You can use upper or lower case in each position.

a HowrnanY

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1il.st,PUg =5/
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uppercase

tr "tffi;'='Uid^f*t

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b. If a password is generated at random find the probability that it consists of all

letters.

n(5)

* 57

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7b 2b 7h

2b

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group of 14 employees (6 women, 8 men) work in the same office. a. In how many different ways can four people be chosen for a project team?
B. Suppose a

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= tcot di@ fu,'*
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b. In how many ways can the team of four people be chosen if it contains exactly3 men and L woman?

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3l^

33

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9. A binary string of length 12 is generated at random. a. Find the probability that the string has exactly four ones.

n

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=

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)

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b. Find the probability that it has at least 10 zeros.

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of -{ust lA zstos z tD t tl rzl Z 7"{1,6 g( tz,]o ) r- c ( tz') t') tC (tzt v) = b6+1 lL+ lZalL
/

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10. In the expansion of (r*y)tu a. Find the term that involv€s y28. (write the coefficient as an integer)

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,?5x, 1 zg

Y=

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other term in the expansion has the same coefficient as your term found in

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(o1a+lzo ffY= X'n,1' =

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and
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11. How many 4-digit base B numbers can be formed if the last digit must be odd and the first digit cannot be 0? Base B numbers can use only the digits from this set {0, L,2,3,4,5,6,7}

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5 have both types. How many of them have at least one of the accounts?

L2. Ata local bank 410 people have a savings account, 640 have a checking account

h(suc) =n(s)+ ^(c)-r,6nC,) : 4tO+ 6,t0*325

= rtven numDer of miles dri ber ot m

7

25 Whh Ja.' ^f !k51 o,1{
Less than 10,000 rniles/yr
75

13. A small delivery company compiled driver accident information for the year 2012. The table below shows the number of accidents for the drivers based on the

10000 or more miler{g.-680 Accident 59s 350 No Accident find the probability that ire a. If a driver is chosen at random from the company, had an accident

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b. Find the probability that the driver drove 10,000 miles or more and did not have an accident.

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c. Find the probability that the driver drove less than 10000 miles'

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Part II (20 points) Answer each question below and give a reason for your answer.
1.

Which is larger C(n,r) or P(n,r)?
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2. Suppose

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,,r7c[,d = ?(!f a sum

two fair dice are rolled. Which is more likely to occur: doubles or

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P
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I

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3.-$ipposei- i coin is tossed 5 times. Which is more likely to occur: exactly 3 heads or more than 3 heads?

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4. If you draw oridfrffiber froFfh-e Sdt-ff7*, occur: an even number or an odd number?

n fr[)Jz

(s): L 2s

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,

f
L

wL,tru

\rlfu-*, Pbwl=*

S

7 ) which is more likely to

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5. . If

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; 1^ wl" 4 ;ufro tbou/'** ppq=t t) ,q 'l Z#r-, ffi/nu'e' PF4=# s,$o^ 6, 8, tol ; a&d"'{'+se It,e, ^ C{LLdr) i-' ,O{.f\r Ca,^J r; {vL{i't i'i,,&tl f,7,5 you choose one card from a shuffled deck, which is more likely to occur: an odd numbered card or an even numbered card? fNote: Ace is not a numbere&card)