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Unformatted text preview: 1:0 12M A . rngfl10686367dougste.11.doc // page 1 of s Tailahassee Community College Name (Last) '@ (First)
MGF 1106 #86367 Spring Semester 2011 I Mr. Jones I Be '3“. 'on 04.18.2011 Test 4A Logic (3. 5 3. 6) & FCP + Prob. (11. 1 11 6.) (100 + 5 possible points)
(Each problem is 5 points). Part 1: (Ch. 3) Multiple Choice. Circle the letter Just the LETTER! of your answer, and then record the letterof your'choice on the line provided. Show all work on any problem that requires it. 1_Seect thf the following statement: N ( A? is: A ML
“if the sky looks blue then it is not nighttime.” 7:; i P If the sky does not look blue, then it is nighttime. A. ® The sky looks blue, and it is night time.
C The sky does not look blue, and it is night time.
D if it is night time, then the sky does not took blue. 35.2 Use DeMorgan s laws to write a statement that' I “Iggyt,“ the following statement "it Is not true that the band does not have a QUI arist and the band plays rock music.” . . . I» (we A t.)
A. The band does not have a guuanst, or the band does not play rock musrc. 3
B. The band has a guitarist, and the hand does not play rock music. ‘ ( P V N i
C. it the band has a guitarist, then the hand does not piay rock music.
The band has a guitarist, or the band does not play rock music. \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ PART 2: (CH 3). SHOW WORK AS NECESSARY. BOX YOUR FINAL ANSWER iN THIS SECTION.
(SOME BOXES ARE PROVIDED). 3. Use this Truth Table to determine whether the symboiic form of the argument is valid or invalid.
g V P
P A q
p —> g — {QEY "" mgf110686367dougstest4a_pll.doc ll page 2 of 5 4. Use a truth table to determine whether the following argument is valid or invalid. (ignore differences in
past, present, and future tense). . , . Dictionary: ' Conclusion: (Circle one)
if I start the diet, lll lose the weight. p: i start the diet. The argument is i don't lose the wei ht. . , . q: I lose the weight.
Therefore, 1 didn t start the diet. @ l NV ALlD 5. Use Euler diagrams to determine whether the foliangargument is valid or invalid. éraw our Euler dia ram in this box.
All silverware are dishwasher safe. y g No candles are dishwasher safe. Therefore, no candles are silverware. Conclusion: (Circle one). The argument is ¢\ INVALID \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ PART 3: (CH 11). SHOW WORK AS NECESSARY. BOX YOUR FtNAL ANSWER iN THIS SECTION.
(SOME BOXES ARE PROVlDED). 6. An ice cream store sells 2 drinks, in 4 sizes, and 8 flavors. in how many ways can a customer order a .
drink? Use the Fundamental Counting Principle (FCP) with three or more groups of items. :5 64
There are ways that the customer can order a drink. 2 *4 ”la 7. How many different combinations of 5 letters can be formed if the first letter must be W or K? Use the
PCP with three or more groups of items. There are different 5letter combinations that can be formed. 2 ﬁerew 2:51] l a
..  arm“ Q»?  {( E Y .__, mgfl10686367dougstest4a_p11.doc // page 3 of 5 8. Evaluate each factorial expression (2/‘1‘120 (o). m) (~~~~~~~1 )1: mo 56 40"”2 :33323! 30 29 28’ ,3» 23 480 320 9. Use the formula P = to solve the following question: (n nir) For a segment of a radio show, a disc jockey can plaercords. if there ar®ecords to select from, 7
in how many ways can the program for this. segment be arranged. )i _ __ 626521309
The program can be arranged in 6'; 652, 800 ways.
10. In how many distinct ways can the letters of the word :‘MEDDLE" be arranged? l $5
6 u 20 .
W“ “ 14*“ ’8“ 11. You volunteer to help drive children at a charity event to the 200, but you can fit oniylof the ﬁchildren present into your van. How many different groups of 7 children can you drive? ‘4
Combo. 3 3 2
I4 Ci 3 12. Use the formula for MC— — —.the FCP to solve the given question. (n— r)!r. In how many ways can a committee of three men and three women be formed from a group of nine men
andsmqggen? Maw: 963 >< ‘63 areas A committee of three men and three women can be formed from a group of nine men and six women in different ways. 13. Us e theoretical probability formula to solve the foliowing problem. Express the probability as a
ractio reduced to lowest terms. (' {J '2) l) i) A 12sided die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6, 7, 8, 9,10, 1 1,12} . Find each
of the following probabilities: m (A). The probability of rolling a1 is (g . (B). The probability of rolling a number less than 12 is . (C). The probability of rolling a number greater than 3 is. (D). The probability of rolling a number greaterthan 21 is n "— KEY, mgfl10686367dougstest4a_p11.doc I] page 4 of 5 r i J J 14.Afaircoin»isto sedtr reetim‘ sin succession. The set of equally iikeiy outcomes is
{HHH HH/TjQiTH, THH HTT THT, TTH TIT}. Give your answer as an integer are simplified fraction. ind the W of getting: B (A). exactly one iaii . i/ 2, (B). a tail on the third toss . (ilint: remember this doesn’t mean a tail on the third toss only!) i t» a it a i; "53”
15. Jim, lan Katrina, Kim Tyrone, Larry, and Simone have all been minted toa dInner party They arrive randomly and each person arrives ata different time e/ order is Imp?“ 1,. ,., 5040 ‘2 (A). In how many ways can they arrive? m 5,, / FT mbsﬂi mi; :2, (B). in how many ways can Jim arrive first and Simone last? '35 $0. 023 309 5233 i (C). Find the probability that Jim will arrive first and Simone last.
(Round off this probability to 4 decimal places). 16. A group consists of six men and seven Women. Three people are selected to attend a conference.
______,__.._... .1_.—. W enter not mini" 5
“Z (A). in how many ways can three people be selected from this group of thirteen? i/ ’3 Ca 286 *1 (B). in how many ways can three women be selected from the seven women? t/ ’5“ C33 1‘; 35
I (C). Find the probability that the selected group wiii consist of ail women. 0. l3? ' \/ 3%; =
(Round off this probability to 4 decimal places). :2: ‘22 3?; 632‘? 17. A city council consists <3me and seven Republicans. is arommr‘aoiusgmgﬁn, people is
selected, find the probability of selecting W and t We (Round off this probability *0 Whose). Cb ﬂ be,
M if a. 356 9.34 and
. M if C a 18. The math depanment of a college base“ 5 male [email protected]%rl;1ale professors/$2 male teaching) assistants and 5 female teaching assrsﬁtysplf a person Is select andom from the group, find the
probabiiity that the selected person is a teaching assistant or BMW pckyour answer as a reduced fraction
W ) \Tﬁ): 73rd [(T‘Aerfeimie) ((12 +5“) + 5)”, 2&3)
Wé’xmmf io'i‘drw 22W :29?
19. One card is randomly selected from a standard deck of 52 cards. (2)921) 1%”
“59
'2 (A). Find the odds in faygr of drawing a spade. The odds are [I] to \/ i3 333 2 i3
_ ' 52
F #3!
‘2_ (B). Find the odds against drawing a Logr. The odds are to I. v 48 :4 F "2‘ 4 “gig”  '32
[ (C). Find the odds against drawing a redgce. The odds are to .v 563 i 2 .. .2 gain 3a ____ KEY ...— mgfl10686367dougstest4awp11.doc ll page 5 of 5 20. The win or of a rafﬂe wiH receive a 78' 8” Bertram 800 yacht. LEOOO rafﬂe tickets were sold and you
purchased 0 ickets, what are the odds against your winning the boat? The Odds aQEL‘LSLW‘an the YBChi are to .(Remember to reduce iprSSIble). W”
ream. $29139 Witt?»
21. (Bonus) If you are given odds of g to :1 in favor of winning a bet, what is the probability of winning the
bet? (Answer as a simptified fraction).  We.”
~4 4: I; F“ 9"”
9 ...
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