Li-j-..~-_-.!!fI, because every element of D I----?--l-~-..-(S-o-

Transcription

1 / ~lj)~ ~eu)ev> l't,l ~ Iq I ~ ~ t II <XI?,tt, "'}1)..3 ()-_ ~ J., t-l (.,,~ to, I~~ 1. Set A is the set of factors of 12, set B is the set of even natural numbers less than 13, set Cis D - 2d 'i c.. 5 the set of odd natural numbers less than 13, and set D Is the set oc even natural numbers less'. - r,, than 7. The universal set is the set of natural numhers less than 13.~ C _ t; I 2.,- ] 9 II J - 7 I -;,,., ) Is DcA? Complete the explanation.!. Lt :. L ',.;/,?, LI, 5"',"',7, 8/~ Li-j-..~-_-.!!fI, because every element of D I----?--l-~-..-(S-o-..-.!ffi] an element oc A. '0I I \ I l;;l 3 2. Set A is the set offactors ofl2, set B is the set of even natural numbers less than 13, set C is the set of odd natural numbers less than 13, and set D is the set of even natural numbers less than 7. The universal set is the set of natural numbers less than 13. What is An C? 3. Set A is the set of factors oc 12, set B is the set of ~ natural numbers less than 13, ~ the set of odd natural numbers less than 13, set D is the set oc even natural numbers less than 7. 'file universal set is the set of natural numbers less than 13. What isa U C? A (1,2,3,4,5,6,7,9, 11,12) B (1,2,3,4,6,7,9,11,12) C (1,3) D (1,2,3,4,5,6,7,8,9, 11,12) 4. You have a set oflo cards numbered 1 tolo. You choose a card at random. Event A is choosing a number less than 7, Event B is choosing an odd number. Calculate the probability of A U B. eta} f 1,2,?/f, ),(" '5. P(A U B)= B '::'f I, =3I '5 J 7/ q ~ It 0 (): ~ 'I :J.. / 3) '1, '>-, icj, 7, 'i5

2 5. Use the complement of the event to find the probability. You spin the spinner sbown. The spinner is divided into 12 congruent parts. Wbat is tbe probability of not spinning a 31 v(~» ~? (3t); 10 Ī&.. Tbe probability of not spinning a 3 Is P(3')= 4 6. A standard deck of cards bas 13 cards (2,3,4,5,6,7,8,9,10, jack, queen, king, ace) in each of suits (bearts, clubs, diamonds, spades). The bearts and diamonds cards are red. Tbe clubs and spades cards are black. You cboose a card from a standard deck of cards at random. Wbat is tbe probability tbat you do ~ not cboose an' n r (- I ) 0r h):!:!... If;) =..!.- i8 Tbe probability tbat you do!,ot cboose a 7 is I- j.. -M 10 '22J 7. You are selecting a card from a standard deck of cards. Matcb each event witb tbe correct probability. Indicate a match by entering tbe letter oftbe event in front oftbe corresponding probability. IJt)).. d~ B. Picking a card that is a spade and an ace C. Picking a card that is not a spade ~nd not an ace. L'111:. J ~ Q(vl 0+ cj.-.')(cl ck ANi) ytot (.LV\, cw:') 13 '5 ~ '> (li'lc l wll-l"9 0.-t~ :3 y')l.'(jit' et(..e S ~ \ - Jig.. -- '5~ >",'~.,.'-.,

3 8. There are 12 runners in a race. Medals are awarded for 1st, 2nd, and 3rd place. In how many different ways can the medals be awarded? - - p- There are 13,;[0 possibilities for awarding medals. IOJ. B-= 9. A clerk has S different letters that need to go in S different envelopes. The clerk places one letter in each envelope at random. What is the probability that ails letters are placed in the correct envelopes? The probabili~ that ails letters are placed in the correct envelopes is ~~(J. 10. Letter tiles spelling the word ENVELOPE are placed into a hag. How many different sequences ofletters can be formed using all the letters in ENVELOPE? The number of different sequences of the letters in ENVELOPE is [JQ]~9:J. 11. A grocer has S apples and S oranges for a window display. The grocer makes a row of the 10 pieces offruit by choosing one piece offruit at random, making it the first piece in the row, choosing a seco~iece offruit at random, making it the second piece in the; row, and so on. What is the probability that the grocer arranges the fruits in alternating order? (Assume that the apples are not distinguishable and that the oranges are not distinguishable.).jq.l, ~ :25;) ~5. _ J. "'-'<H-f' - The probability that the grocer arranges the fruits in alternating order is?l;ls;}-: 'II?-(". 12. There are 8 books numbered 1-8 on the summer reading list. Peter randomly chooses 2.boo!<s. What is the probability that Peter chooses b9dks numbered 1 and.2, in either order? ;;l./ 8 P~ _. ')./ I IS(" The probability is 1;;{Y: that Peter chooses books numbered 1 and 2, in either order. 13. On an exam, students are asked to list,!.historical events in the order in which they occurred. A student rand9ntly_orders the events. whitt is the probability that the student chooses the correct order? The probability that the student chooses the correct order is,...l. ~,;(t4 I - cqt)~_.

4 ;. -t<(fl"' 10~ (Y'tJ-- t+ IY CQl1\.C ina. J-w'"'"I l,ij duo" "\,r r..' 110.;-;( ~r' ) /U ~~ oan amusement park has14 roller coasters. In how many ways can you choose 4 of the roller coasters to ride during your visit to the park? )t..j [1 ::.,(rd ( There are L-.-L~ J different ways you can ride 4 of the roller coasters during your visit to the park A bouquet of6 flowers is made up by randomly choosing between~s and carnations. What is the probability. the bouquet will have at most 2 roses? Enter your answ;; as a fraction in simplest form.. ;;J. Ct> 0C 61' '_ I OS/ &<-1 There is a probability of ;;Z -:f/fr;lj: \'13 ~ that the bouquet will have at most 2 roses. (p Col -=- 4J / tr4 I IvA ~ :l;;k'i 1\ (~~~ ;) -;';;z.o'"i 16. You flip a coin l~s. What is the probability that you get at most 3 heads? Enter r )(.,(- your answer as a fraction in sijnplestform.. p( )(.s. '3 Ju:~) Ii v'3', ) 013;;1. ~ I' C"J.'..,':i There is a probability of ~8' ~ % 2"lD that the flipped coins will have 3 heads I I(I" I\ at most.. I. (I(0' I..--!~'"h -01~~ 17. There are 12 peaches and 8 bananas in a fruit basket. You get a snack f~ and thr~e of your friends b--.wosin four of the ieces offruit at random. What is C. _ i igtj)- (}D if - -, There is a probability of "\Cj.)h'f:) that all 4 are peaches. --, Your teacher chooses 2 students at random to represent your homeroo!j\. The homeroom has a total of ~tudents, inclul!jng your 6est fri~nd. What is the probability that you and your best friend are chosen? Enter your answer as a fraction. There is a probability of \('10 Co that you and your best friend are chosen. 19. There are 29 students In your class. Your science teacher will choose ~ students at random to create a "Iq t group to do a project. Find the.probabillty that you and you~ 2 best friends in the science class will be ~~C.?~~ chosen to be in the groue. Enter your answer as a fraction In simplest form. ~ t:),; \~ J. There is a?//$;)..'/ probability that you and your 2 best friends will be chosen. Q(Pc.;;.. - q c. 'J.-. 5

5 \}.,v c;\g i\\l, our teacher chooses 2 students at random to represent your homeroom. The homeroom has a total ~. of 29 studeuts, including your best friend. What is the probability that you and your best friend are chosen? Enter your answer as a fraction. There is a probability of that you and your best friend are chosen. ~l[;'i0-. \) ;6:"There are 29 students in your class. Your science teacher will choose 5 students at random to create a. group to do a project. Find the probability that you and your 2 best friends in the science class will be chosen to be in the group. Enter your answer as a fraction in simplest form. There is a probability that you and your 2 best friends will be chosen. 21. On a television game show, q members of the studio audience are randomly selected to be eligible contestants. Part lout of2, Six of the 12 eligible contestants are randomly chosen to playa game on the stage. How many combinations of 6 players from the group of eligible contestants are possible? There are L ~.,2iOrJcombinations of 6 players. 22 Determine whether it would be better to use permutations or combinations to find the number of possibilities in each of the following situations. Select the correct answer for each lettered part. A) Selecting a group of 6 people from a group of9 people. B) Finding the number of coi~biilations for a combination lock. Lp~~idj] C) Awarding first and second place ribbons in a contest. L~.f 1>1.,<.-1- Jil D) Choosing 3 books to read in any order from a list of 7 books. Ltg~_~Jil

6 f C ljyyl~\i Ltc--h.J:-h ((71 p~(i'lv" eaj~(\t-.s 23. Using the lellers A, B, and C, complete the explanation of the difference between a permutation and a combination. In I.~ L'Yl'VD jet order does not matter. In Lpe(J~+.'"!iifl,order does mailer. In a L.e:e.r Ol:~~~jgJOf A, B, and C, ABC is different from CBA, so they would be counted as two different I_,_t~ l l.in L~~jJJ.I~"':"!. lrj,abc is the same as CBA, and would not be counted agaio. ' '. 24. Calculate I2C7and I2C" What do you notice about these values? Complete the explanatioo on why this makes sense. I2c7=1 ~~ I2C,=L_15~. It makes sense that tbese values are L---(1 k.~l_@!jbecause every combination oft I._job)ects that are selected bas a corresponding combination ofs objects tbat are not selected. Use your observations to help you select a generalization about combinations. A B nc, = nc,xn nc, = ncr+ n cd ncr = ncn-r D nc, =,-ncn C- /5 '3