You are packing fo a vacation. At home you ha e 10 shirts and 7 airs of shorts.


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1 LESSON 12.3 Name WarmUp Exercses For use before lesson 12.3, ages Avalable as a transparency You are packng fo a vacaton. At home you ha e 10 shrts and 7 ars of shorts. 1. In how many dfferent ways can you choose 4 pars of shorts to take on vaca on? 2. In how many dfferent ways can you choose two shrts to wear on the frst and second days of vacaton? 3. If you brng 4 pars of shorts and 6 shrts, how many dfferent outfts can you make? Daly Homework Quz For use after Lesson 12.2, pages Fnd the number of combnatons C4 Wrte the bnomal expanson. 3. (x + 3)4 4. (3  >>)3 42 Copyrght McDougal Lttel! Inc All rghts reserved l
2 LESSON 12.3 Name Applcaton Lesson Opener For use wth pages Avalable as a Imsparency The probablty of an event s a number between 0 and 1 that ndcates the lkelhood that the event wll occur. Some sample probabltes and ther meanngs are gven below. P = 0 Event wll not occur. P Event probably wll not occur. P = 0.5 Event s equally lkely to occur or not occur. P 0,75 Event probably wll occur. P 1 ' Event s certan to occur. St te hether the robablty that the event wll occur s closer to 0, 0.25, 0.5, 0.75, or The next tme you flp a con, t wll come up heads. 2. The frst card you draw from a standard 52card deck wll be a heart. 3. The next baby bom n your town ll be a grl. 4. There wll be a snowstorm n Oho n My. 5. The next tme you roll a number cube, you wll get an odd» number. 6. You wll be assgned homework n the next week. 7. The frst card you draw from a standard 52card deck wll be a 7, 8, or You wll attend school on My The frst card you draw from a standard 52card deck wll be a spade, club, o damond. Copyrght McDougal Lttell Inc All rghts reserve. 43
3 Name Pract ce A For use wth pages Spnnng a Spnner You have an equally lkely ch nce of spnnng any value on th spnner. Fnd the probablty of spnnng the gven event 1. a shaded regon 2. a factor of a number less than 6 or a shaded regon 4. an even number or perfect square 5. a prme nu ber 6. a twodgt number Choosng Marbles A jar contans 5 red matbles, 3 green m rbles, 2 yellow marbles, nd 1 blue marble. Fnd the probablty of randomly drawng the gven type of marble. 7. a yellow marble 8. a blue arble 9. a green or yellow marble 10. a red or ellow marble School Mascot In order to choose a mascot for a new school, 2755 students were surveyed 896 chose a falcon, 937 chose a ram, and 842 chose a panther The remanng students dd not vote. A student s chosen at random. 11. What s the prob blty that the tudent s choce was a anther? 12. hat s the probablty that the student s choce was not a ram1? 13. Wh t s the probablt that the student s choce was ether a f lcon or a ram? Httng a Star n E ercses 1416, use the followng nformaton. You are throwng a dart at he sq are shown at the rght. Assume that the art s equally l ely to land at any pont n the s uare. The square s 2 nches by 2 nches. Each sta has an area of 0.01 square nch. 14. The d rt has landed nsde the squae. What s the probablty that t ht a star? 15. The dart has la ded nsde the square. What s the probablty that t ht a star m the top three rows? 16. The dart has l nded nsde the squ e. What s the p obablty that t h one of the four corner stars9 x ' x L so 12 3 Copyrght McOougal Lttel Inc All rghts reserved Chapter 12 Resou ce Book 45
4 Name Practce B For use wth pages 71&722 Choosng Numbers You have an equally lkely chance of choosng a y nte ger from the set {1,2, 3,4,5,6,7, 8,9,10,11,12}. Fnd the probablty of the gven event. 1. An even number s chosen. 2. A prme number s chosen. 3. A multple of 3 s chosen. 4. A twodgt number s chosen. Farm Anmals Your cousn lves on a small farm. She a ember of the 4H Club and s sho ng nne anmals at the county far. T o of her anmals won a blue rbbon (1st place), one won red nbbon (2nd place), and three won hte rbbons (3rd place). You do not know whch anmals won whch przes. You choose one of your cousn s anmals at random. 5. What s the robablty that the anmal won a 1st place rbbon? 6. What s the probablty that the an l won a rbbon? 7. What s the probablty that the anmal won a red or whte rbbon? Lve Brths In Exercses 810, use the followng nformaton. Of all lve brths n the Unted States n 1996,12.9% of the mothers were teenagers, 51.8% were n ther twentes, 33.4% were n ther thrtes, and the rest were n ther fortes. Suppose a mother s chosen at random. 8. What s the probablty that the mother gave brth n her twentes? 9. What s the probablty th t the mother gave brth n her twentes or thrtes? 10. What s the probablty that the mother gave brth n her fortes? 11. Choosng Cons You have 8 pennes n your ocke dated 1972,1978, 1979, 1985, 1989, 1991, 1993, and You take the cons out of your pocket one at tme, What s the probablty that they are taken out n orde by date? 12. Geometry Fnd the prob blty that a dart thrown at the gven target wll ht the shaded regon. Assume the dart s equally l ely to ht any pont nsde the target. Copyrght McDouqal Lttel Inc. All rghts reser ed
5 Name Reteachng wth Practce For use wth pages f ' : Fnd theoretcal and expe mental probabltes Vocabulary The probablty of a event s a number between 0 and 1 that ndcates the lkelhood the event wll occur. Theoretcal probablty s a type of probablty that s based on al outcomes of an event A beng equally lkely, and s gven by number of outcom s n P(A) = total number of outcomes Experment l robablty s a type of p obablty that s based on the results of a ex erment, a survey, or the hstory of an event. fllfll Fndng Probabltes of Events You dra a.card from a standard dec of 52 cards. Fnd the probablty of dr wng a face card. So uton T elve outcomes corres ond to drawmg a face card: J, Q and K from the four suts. k / drawng a face cad) Exercses for Example 1 Sm lfy the expresson. numbe of ways o dr a face card _ 12 number of ways to d aw a card 52 _3_ Fnd the probablt of choosng an E when selectng a letter from those n the word COLLEGE 2. A card s drawn f om a standard dec of 52 cards. Fnd the robablty the card s ether a club o a spade. Probabltes nvolvng Permutatons and Combnatons For next year s schedule of cl sses, mathematcs, Englsh, hstory, and scence are each scheduled durng t e frst four erods of the day. Your sc edule s andomly selected by a computer. a. What s the robablty tha En lsh, math, scence, and hstory wll be scheduled m that order? b. Your favorte subjects a e math and scence. What s the probablty that your favonte subjects wll be scheduled the frst two perods, n * any order*? R Copyrght McDougal Lell Inc All rghts reserved 1 I
6 LESSON CONTINUED Name Reteachng wth Practce For use wth pages Soluton a. Because there are four subjects, you have fo r choces for frst perod, three choces for second perod, two c oces for thrd perod, and one choce for fourth erod. So, there are 4! dfferent ermutatons of subjects. Because there s only one way to schedule your classes wth Englsh f st, math second, scence thrd, and hstory fourth, P(E,M, S,H) = ~ = = b. There are 4C2 df erent combnatons of 2 subjects. Of these 2C2 contan 2 of your favorte subjects. So, the probablty s: 1 C 1 P(schedulng 2 favortes frst) = ~~ = C2 6 Exercses for Example 2 Seven letters are chosen, one at a tme, at random from those n the word ENGLISH. 3. Fnd the probablty that they ll be chosen n alphabetcal order. 4, Fmd the probablty that the frst letter wll be a vowel. Fndng Expermental Probabltes In order to choose a masco for a new school, 1847 students were sur ve ed: 529 chose falcon, 762 chose a ram, and 501 chose a panther. The remanng studen s dd not vote. If a student s selected at random, what s the probablty that the student s choce was a anther7 Soluto Of the 1847 students surveyed, 501 chose a panther. So, the probablty s: L sson 1?.3 P(panther) = «0.271 Exercses fo Example 3 hrt students n an class took a test: 8 receved A s, 13 receved B s, and 9 receved C s. If a student from the class s r ndo ly chosen, 5. What s the probablty the s udent receved a C on the test? 6. What s the robablty the student receved an A or B on the test? Copyrg t McDougaf Lttell nc nghts reserved 49
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