Probability The Language of Chance P(A) Mathletics Instant Workbooks. Copyright

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1 Proility The Lnguge of Chne Stuent Book - Series L-1 P(A) Mthletis Instnt Workooks Copyright

2 Proility The Lnguge of Chne Stuent Book - Series L Contents Topis Topi 1 - Lnguge of proility Topi 2 - Smple spe Topi 3 - Outomes Topi 4 - Multi-stge events listing outomes Topi 5 - Multi-stge events etermining outomes Topi 6 - Investigting outomes Dte omplete Prtie Tests Topi 1 - Topi test A Topi 2 - Topi test B Author of The Topis n Topi Tests: AS Klr Proility The Lnguge of Chne Mthletis Instnt Workooks Series L Copyright 3P Lerning

3 Proility The Lnguge of Chne Topi 1 - Lnguge of proility Using the terms of proility, rte these events s ertin, likely, unlikely, impossile or even hne. The sun will rise tomorrow A lion hving four legs If ie is rolle, seven ppers Mony will follow Suny next week e Suny will follow Mony next week f John will live to the ge of 142 yers g Soring n even numer when ie is thrown h A yer hving 460 ys Selet the most pproprite from 0%, 30%, 50%, 70% n 100% to esrie the hne implie y eh of the following wors. mye efinitely perhps sure e n outsie hne f g ginst ll os h proly Choose from ertin, most likely, even hne, unlikely or impossile to est esrie n event whih hs proility of: 10% 0 100% 7 8 e 1 2 f 95% g h 3 97 i 4 5 j 1 k 1 64 l 75% Proility The Lnguge of Chne Mthletis Instnt Workooks Series L Copyright 3P Lerning 1

4 Proility The Lnguge of Chne Topi 2 - Smple spe Rolling ie one Write the smple spe for eh of the following. Tossing oin one Choosing letter from the lphet Choosing vowel e Choosing igit from the ounting numers less thn 10 f Seleting 10 from norml pk of plying rs g Seleting y of the week h Seleting month of the yer The letters of the wor WOOLLOOMOOLOO re written on rs n turne fe own. A r is then selete t rnom. Write the smple spe. How mny elements hs the smple spe? How mny ifferent elements re in the smple spe? For eh of the following proility experiments, write the numer of elements in the smple spe. Seleting r from norml pk of 52 plying rs. Seleting ll rwn in Lotto rw. (The lls re numere 1 45.) Seleting the winner of 12 horse re. Seleting numer from 1 to 500 inlusive. Proility The Lnguge of Chne Mthletis Instnt Workooks Series L Copyright 3P Lerning 2

5 Proility The Lnguge of Chne Topi 3 - Outomes For eh of the following, stte whether eh element of the smple spe is eqully likely to our. Rolling ie Tossing oin Choosing letter from the lphet Seleting r from norml pk of rs e Choosing igit from the ounting numers less thn 10 f g h The result of tennis gme etween two plyers Winning the first prize from rffle with 500 tikets Tossing two oins t the sme time Write the outomes for eh of the following. Seleting letter from the wor PROBABILITY. Seleting mrle from g onsisting of white mrles only. A letter from X to Z. A letter fter Z. A r is rwn from norml pk of rs. How mny outomes re there for eh event elow? e f g h A queen A piture r A re r A spe A re ten A five of lus A nine or ten A lue jk Proility The Lnguge of Chne Mthletis Instnt Workooks Series L Copyright 3P Lerning 3

6 Proility The Lnguge of Chne Topi 4 - Multi-stge events listing outomes One re, one lue n one white ll re in ox. The lls re remove, one t time, n ple in row. List ll the possile outomes. How mny ifferent possiilities re there for the first ll? One the first ll hs een hosen, how mny possiilities re there for the seon ll? One the first two lls hve een hosen, how mny possiilities re there for the lst ll? The numers 1, 2, 3 n 4 re written on 4 rs, one on eh r. The rs re shuffle n then ple sie y sie to form 4-igit numer. List ll the possile outomes. How mny outomes re possile? If fifth r, with the numer 5 on it, is e n the 5 rs re now shuffle n ple sie-y-sie, how mny ifferent 5-igit numers re possile? Justify your nswer. The letters A, B n C re written on three rs, one on eh r. The rs re shuffle, one r is selete, the letter is written on lkor n then the r is reple. The rs re reshuffle n nother r hosen, the seon letter eing written esie the first n the r reple. Agin the rs re reshuffle n thir r is rwn n the thir letter is written on the lkor esie the other two. List the possile outomes. How mny outomes re possile? If 4 th r ws selete in the sme wy, how mny totl possile outomes re there? If 8 seletions were me, how mny possile outomes woul there e? Justify your nswer. Proility The Lnguge of Chne Mthletis Instnt Workooks Series L Copyright 3P Lerning 4

7 Proility The Lnguge of Chne Topi 5 - Multi-stge events etermining outomes Some r numer pltes onsist of three letters, followe y three igits. How mny ifferent numer pltes of this type re possile? In ountry town ll telephone numers hve 8 igits. If the first five igits must e the sme for every phone numer in the town, how mny ifferent phone numers re possile? A smll fé serves two-ourse lunhes n three-ourse inners. The lunh menu hs three hoies for the min ourse n three ourses for essert. How mny ifferent twoourse lunhes re possile? The inner menu hs four hoies of entrée, five hoies for the min mel n three hoies for essert. How mny ifferent three-ourse inners re possile? QUESTION 4 Eh prtiipnt t sports rnivl ws ientifie y oe numer. This oe numer onsiste of letter of the lphet followe y single igit numer. How mny prtiipnts oul e ientifie y this metho? Question 5 To ess informtion from lu s omputer, eh memer ws require to hoose psswor of 4 hrters. Eh hrter oul e either letter of the lphet or igit from 0 to 9. How mny ifferent hrters re there? How mny possile psswors re there? Question 6 There re seven lls in ht, eh ientil exept they re numere from 1 to 7. The lls re rwn t rnom, one fter the other without replement, n ple on rk to form sevenigit numer. How mny ifferent seven-igit numers oul e forme? Proility The Lnguge of Chne Mthletis Instnt Workooks Series L Copyright 3P Lerning 5

8 Proility The Lnguge of Chne Topi 6 - Investigting outomes Brney ws onsiering uying house tht he knew oul e ffete y one-in--hunreyer floo. Brney re in the lol pper tht suh floo ourre in He onlue tht he oul uy the house n e sfe from suh floo for quite few yers. Do you gree with Brney? Disuss. Ann eie to enter tlent quest. Either I will win or I won t, she si. Therefore, I hve hne of winning. Briefly explin wht is wrong with Ann s sttement. Ken ws plnning holiy to region tht lime to reeive snow on hlf the ys eh yer. Ken onlue tht he oul expet it to e snowing on hlf the ys of his holiy. Do you gree? Justify your nswer. QUESTION 4 If I hoose letter t rnom from the lphet it oul either e vowel or onsonnt. Therefore I hve hne of hoosing onsonnt. Is this sttement true or flse? Disuss. If I hoose letter t rnom from the pge of ook, it oul either e vowel or onsonnt. Therefore I hve hne of hoosing onsonnt. Is this sttement true or flse? Disuss. Proility The Lnguge of Chne Mthletis Instnt Workooks Series L Copyright 3P Lerning 6

9 Proility The Lnguge of Chne Topi Test PART A Instrutions This prt onsists of 8 multiple-hoie questions Eh question is worth 1 mrk Clultors my e use Fill in only ONE CIRCLE for eh question Time llowe: 20 minutes Totl mrks = tikets re sol in rffle. One tiket is rwn t rnom to win first prize. Json ought five tikets in the rffle. His hne of winning first prize is: A impossile B unlikely C likely D ertin 2 Two ie re thrown together n the numers on the uppermost fes e together. How mny elements re in the smple spe? A 6 B 11 C 12 D 36 3 Shne trvels from P to Q to R. He hs the hoie of 4 routes from P to Q n 5 routes from Q to R. How mny ifferent routes n Shne tke when trvelling from P to R? A 1 B 9 C 20 D 45 4 Employees t ompny eh hve n ientity numer tht is me up of letter of the lphet followe y two-igit numer (from 00 to 99). Wht is the mximum numer of employees tht oul e ientifie using this system? A 2340 B 2574 C 2600 D There re 37 slots on roulette wheel; 18 re, 18 lk n one green. An experiment is onute y spinning the wheel 50 times n reoring the olour of the slot on whih the wheel lns. The numer of ifferent outomes in the smple spe is: A 3 B 18 C 37 D 50 6 Whih event hs hne of hppening? A B C getting two hes when tossing two oins getting n o numer when throwing ie getting piture r when hoosing r from stnr pk of rs D rnomly piking the winner of 5 horse re 7 Whih outomes re not eqully likely? A the result from tossing fir oin B C D the result from throwing fir ie noting the suit when rnomly seleting r from stnr pk the olour of the trffi light when rehing n intersetion Proility The Lnguge of Chne Mthletis Instnt Workooks Series L Copyright 3P Lerning 7

10 Proility The Lnguge of Chne Topi Test PART A 8 The four es from stnr pk of rs re shuffle n ple fe up in row. How mny ifferent rrngements re possile? A 4 B 10 C 24 D 256 Proility The Lnguge of Chne Mthletis Instnt Workooks Series L Copyright 3P Lerning Totl mrks hieve for PART A 8 8

11 Proility The Lnguge of Chne Topi Test PART B Instrutions Show ll neessry working Totl mrks = 7 9 The numers 7, 8 n 9 re written on three rs, one on eh r. The rs re shuffle n then ple fe up in row. List ll the possile rrngements. 1 mrk Another r, with the numer 5 on it, is e. The four rs re shuffle n ple fe up in row. How mny ifferent rrngements re possile? 1 mrk 10 On ny given y you n either e well or ill. Therefore you hve hne of eing sik on ny y. Comment riefly. 2 mrks 11 The letters A, B, C, D, E n F re written on 6 rs, one on eh r. The rs re shuffle. One r is selete t rnom n ple on tle. A seon r is then rnomly selete n ple esie the first. The proess is ontinue until 5 of the 6 rs re on the tle. How mny ifferent rrngements re possile? 1 mrk Briefly esrie in wors the likelihoo tht the rs spell out the wor FACED. Justify your nswer. 2 mrks Proility The Lnguge of Chne Mthletis Instnt Workooks Series L Copyright 3P Lerning Totl mrks hieve for PART B 7 9