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SampleTest1solutions

# SampleTest1solutions - p.1 1 A hat contains 3 red slips of...

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Unformatted text preview: p.1 1) A hat contains 3 red slips of paper and 2 green slips of paper. One slip after another is drawn from the hat, without replacement. The colors of the drawn slips as well as the order in which they were drawn is recorded. The process is terminated whenever the same color is drawn twice in a row or there are no more slips left in the hat. What is the size of the corresponding sample space? Hint: Draw a tree. Example: One outcome would be RGRGR (red, then green, then red, then green, then red), another is GG. TRE€J p.2 2) Adam, Barb, Candy, Doug, and Earl go to the movie theater and sit in a row with exactly 5 seats. How many different ways can they arrange themselves? 53 { PM\sxwiiqvxmijEWﬂaa‘dw. Dwaywmr 5‘4‘3'Z"h\2'0 ‘ S . ' 2’; S! '*: t 3. X 0A, P(S,§)' (5'5)! ”ET ‘" m 20 p.3 3) You roll two fair dice and look at the result. What is the probability that you do not see a 1 or a 2 on either die? Example: Rolling a 4 on the ﬁrst die and a 5 on second — neither die came up with a 1 or 2. IN sin-«Pu: SPAC£ 0dAa’U~»M.m M w M M W 0L L011 WW». Tm. (pov‘l‘t‘l W 24 4 a: y .92.... {W' 3g :36, W TVPleL, ELEMENT p.4 4) Find n(A H B), given that A and B are subsets of U with n(U) = 1007 n(A’) = 77, n(B) = 15, and n(A U B) = 31. L h(A'\=‘77 :37 MM : h(,U)-MA{) ':~Mo-71=23 ‘mlAUBX: MAHMMV MAAB) 3\ 1' 2.3+‘S“h(b.(\ﬁ) :5 MAM“): 23+t3~31=7 a... a...» w 5) YOu are casting a play. There is one female role to be cast: Old Mother Hubbard. And there are three male roles to be cast: the Butcher, the Baker, and the Candlestick Maker. 3 women and 4 men try out. How many ways can you cast the play? mg,“ l I 14):»; 7‘ t. # tanks“; , pc4’93‘ﬂ Wu sJLSLHi 4 WH¥13W 1/>3%WW,WW aw” OW 3,4,3,Z:1 p. 6 6) Of a group of 100 people, 15 smoke, 42 drink coffee, and 3 smoke but don’t drink coffee. HOW many drink coffee but don’t smoke? 7 ' Hts) “5 l5 In (C) 31' 42 \ML nkgoli U/u. h(53¢ 4L 7) HOW many 5 digit numbers are there that consist of only 4’8 and 8’s? Examples: 44888, 44444, 84848, 84444. ZJNM 2W . ZYZ}Z“2XZ =3 \$2 p.8 8) Let A, B, C be subsets of a universal set U where n(U) = 412. Shown below is a Venn diagram for the sets A, B, C (which has been labelled with the number of elements in its various subsets). How many elements are in the set (A’ U B’ U 0’)? Am (A’UB‘ u cf) =' CAMS“)! “C Mmsndzlt "9 thAnBOC\')= huh—Mammal a.” - Adz 44> : £653. W p.9 9) Suppose (2 is a uniyersal set with 71(9) 2 100, and suppose A, B, and C are subsets of Q with: n(A) 2 72(8) 2 11(0) = 50 , n(A F] B) : n(B ﬂ 0): n(A 0 C) ‘= 30 “(IO n((AUBUC)f = 22 1 What is n(AﬂBﬂC)? MN) 1500 : MAM nus) + Me) —~ “(A033 wane] ~«(Ancwmmnw6 WmmeM M -~—W‘ W [jg-1" ‘50 " %0 + hCPHWSDCA 78 -: 9:) + hCANﬁHQ) =9 “(Amend)”? V8 10) A hat contains 5 red slips of paper and 7 green slips of paper. Two slips are drawn out of the hat, at random, one after the other, and without replacement. What is the probability that both slips are red? (tam CU? ! 2) \ Wm WW‘Wvd“ ngw 51%, to T . ' 66 ‘7’”), p. 10 11) How many 3 letter words can be formed using the letters AABBCCDDEEFF? Example: Here are some 3 letter words that can be formed: ACA, FDC, EBC. Hint: How many 3 letter words are possible using the letters AAABBBCCCDDDEEEFFF (i.e. there are no “restrictions” )? W‘II ' “I 3;». get me 3 WW WWWgﬂ:\W&J TMMQ i W Ammuem a. w) grep WWW; meme :2”: 12) Ima Quack has 6 patients in the waiting room, 2 men and 4 Dr. Quack sees a male patient and then a female patient? p. women. One patient is selected at random to see Dr. Quack and then another (at random). What is the probability that 12 p. 13 13) Five boys and two girls are seated in 7 seats numbered 1 through 7. In how many ways can this be done so that the 2 girls are seated in seats 1 and 2? TM 0% 2 ”W7?!“ wt WWIE; {as m aw ammo-M. I4 MW Maw 55 Mew ”WW-[\$0. PFJQLJWZ 4% W)! (Dz/W: 22-53,:- gamma p. 14 14) A six-sided die is weighted so that rolling a 1,, 2, 3, and 4 are equally likely and rolling a 5 is 2 times as likely as rolling a 4 and rolling a 6 is 2 times as likely as rolling a 4. What is the probability of rolling a 2? \UU\ + wczA f wLZ‘) + wL‘H + wif§\ ~+ wuﬂ‘l "4 % x-VU'L4) Hum) + WM) +ur[4l 1.» ZLUL4\ + Zwm :l m”) gummy as) mam "Ag w?) WLZ\= V2 ”a p. 15 15) You own 3 cars. Each [S to be painted either red, or yellow, or black, or white In how many ways can this be done 1n such a way that exactly 2 or the cars are the same color? Examples: One way is to paint car 1 black car 2 white, car 3 black Another way is to paint car 1 red, car 2 red, and car 3 black. WM l j, - W 2 me% Willi, W11, helm, TM M1,, ’ ”27:53, W” mm (11. m, m sum “91%,, M 2 Mm_.Tlm, We. iclm. TMull—«Xio. Cebu 5mm Awwmg W191 Thu QM, g M, Mt .mea , Wm: 3145:36 W2 Tmmqwe Q4W&A%W%%M WW Oldwtaé‘lw; Einwmﬁrsz 24 WQ?:§W MJJRK Mw‘wg‘“ ("Chm a." W.Miaiu OWL ' WM . Aim“? 4 why PM (IMAM GUM lit-«1,,- “13m“ MEN” TM Wm: 0% ® ”Mel (9 W Lb“ @ﬂhmﬁ ng 2 Mitre,» “WM Whey WAMM W4»; Q4‘(2fl+‘l\: G), @ "3-1" ...
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SampleTest1solutions - p.1 1 A hat contains 3 red slips of...

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