# Probability and Statistics P(A) Mathletics Instant Workbooks. Copyright

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1 Proility nd Sttistis Student Book - Series K- P(A) Mthletis Instnt Workooks Copyright

2 Student Book - Series K Contents Topis Topi - Review of simple proility Topi - Tree digrms Topi - Proility trees Topi - Dot digrms Topi 5 - Venn digrms Topi - Review of sttistis Topi 7 - Mesures of spred, stndrd devition Topi 8 - Mesures of spred, interqurtile rnge Dte ompleted Prtie Tests Topi - Topi test A Topi - Topi test B Author of The Topis nd Topi Tests: AS Klr Mthletis Instnt Workooks Series K Copyright P Lerning

3 Topi - Review of simple proility QUESTION A rd is drwn t rndom from norml pk of 5 rds. Find the proility tht the rd is: lu lk rd n e d not spde e lk e f red rd QUESTION From the letters of the word CHANCE, one letter is seleted t rndom. Wht is the proility tht the letter is: vowel? onsonnt? the letter C? QUESTION A die is thrown one. Find the proility tht the numer is: five n odd numer numer greter thn d zero e prime numer f squre numer QUESTION A g ontins yellow, lue nd 5 red lls. If ll is drwn t rndom, find the proility tht it is: yellow red lue d not yellow e white f either lue or red QUESTION 5 A three-digit numer is to e formed from the digits, 5 nd written on three seprte rds. Wht is the proility tht the numer: formed is even? is odd? is less thn 500? d is divisile y? e is divisile y 5? f is greter thn 00? QUESTION The numers to 7 re written on seprte rds. One rd is hosen t rndom. Wht is the proility tht: the numer is odd? the numer is even? it is? d it is zero? e it is prime numer? f it is divisile y? QUESTION 7 A letter is hosen from the word PROBABILITY. Wht is the proility tht the letter is: vowel? onsonnt? the letter B? d the letter P or B? e the letter M? f the letter Y? Mthletis Instnt Workooks Series K Copyright P Lerning

4 Topi - Tree digrms QUESTION A oin is tossed three times nd the results noted. Use tree digrm to find the proility of: three heds two heds nd one til in ny order t lest one hed QUESTION d There re four rds mrked with the numers,, nd. They re put in ox. Two rds re seleted t rndom, one fter the other, to form two-digit numer. Drw tree digrm to find: how mny different two-digit numers n e formed the proility tht the numer formed is less thn the proility tht the numer formed is divisile y the proility tht the numer formed is even QUESTION Three red lls nd two lue lls re pled in g. Two lls re seleted t rndom, without replement. Wht is the proility of hving: two red lls? two lue lls? one red ll nd one lue ll? QUESTION In fmily of three hildren, use tree digrm to find the proility of: three oys two oys nd one girl one oy nd two girls d the eldest hild eing oy e the youngest hild eing girl f three girls Mthletis Instnt Workooks Series K Copyright P Lerning

5 Topi - Proility trees QUESTION d e A ox ontins yellow nd 5 lk lls. A ll is drwn from the ox nd is not repled, then seond ll is drwn. Find the proility of: yellow then lk eing drwn lk then yellow eing drwn oth lls eing yellow oth lls eing lk drwing yellow nd lk in ny order QUESTION Din hs ox ontining three red nd two green mrles. She selets two mrles t rndom. Find the proility of two green mrles if she reples the first mrle efore she drws the seond. Roger uys three tikets in rffle in whih there is totl of 0 tikets. There re two prizes. Find the proility of him winning: first prize first prize only oth prizes no prizes t lest one prize one prize only QUESTION d e f QUESTION A jr ontins five white nd six red jelly ens. Kylie tkes en t rndom nd ets it. She then tkes nother jelly en nd ets it. Wht is the proility tht: the first en eten is white? the two ens eten re oth red? Mthletis Instnt Workooks Series K Copyright P Lerning

6 Topi - Dot digrms QUESTION A pir of die is rolled simultneously. Complete the digrm to show the totl numer of smple points. The first olumn hs een done for you. smple oints p 5,,,, 5, 5, QUESTION Use the ove digrm to find the proility of eh event listed elow. doule three ny doule totl of 9 d sum greter thn 0 e sum of either or f sum less thn 5 g the sum of the numers is 7 h the two numers re odd i the sum of the numers is 0 j t lest one k the sum of the numers is greter thn QUESTION Suppose we wish to throw totl of. Whih is the etter hne rolling one die or two die? QUESTION Wht is the proility of rolling two even numers in one roll of pir of die? QUESTION 5 A oin nd die re thrown simultneously. Find the proility of throwing hed nd n odd numer. QUESTION If we wnt to throw sore of, whih would give etter hne rolling one die or two die? Mthletis Instnt Workooks Series K Copyright P Lerning

7 Topi 5 - Venn digrms QUESTION From norml pk of 5 plying rds, one rd is seleted t rndom. Drw Venn digrm to find the proility of the rd eing either lk rd or n e. QUESTION The numers from to 5 re written on 5 rds nd out of these rd is hosen t rndom. Drw Venn digrm to find the proility of the numer on the rd eing: less thn or divisile y 5 less thn 7 or divisile y QUESTION doule or totl of 0 Two die re thrown simultneously. Drw Venn digrm to find the proility of: totl tht is either odd or less thn QUESTION From pk of 5 plying rds, rd is seleted t rndom. Drw Venn digrm to find the proility of it eing hert or queen. Mthletis Instnt Workooks Series K Copyright P Lerning 5

8 Topi - Review of sttistis QUESTION Fifty fmilies were surveyed to find how mny hildren eh fmily hs nd the following set of dt ws otined d Complete the frequeny distriution tle. Drw frequeny histogrm. Drw frequeny polygon. Drw umultive frequeny histogrm. Sore (x) 0 Tlly Frequeny (f ) Cumultive frequeny e Drw umultive frequeny polygon. 5 Σf = Frequeny Cumultive frequeny Sore Sore QUESTION For the frequeny distriution given ove, lulte: the men the mode the rnge d the medin e the reltive frequenies Mthletis Instnt Workooks Series K Copyright P Lerning

9 Topi 7 - Mesures of spred, stndrd devition QUESTION Use your lultor to find the men nd stndrd devition, orret to one deiml ple, for the following sets of sores. Also find the rnge of eh set of sores.,, 8, 0,,,,, 7,,,,, 8 d, 8, 0,,,, 7 e 8,,, 8, 8,,,,, f 8, 0, 0, 8, 8, 0, 8, 0, 5 g Sore Frequeny h Sore Frequeny 5 QUESTION d Five students st for mthemtis test nd siene test. Their mrks re given elow. Siene Mthemtis Find the men nd stndrd devition for eh set of sores. Mihel sored 9 in siene nd 8 in mthemtis. Whih ws the etter mrk? If Mtthew sored 5 in siene nd 80 in mthemtis, in whih sujet did Mtthew perform etter ompred with the lss verge? Use your lultor to find the stndrd devition nd the men for eh test. Test A Test B For whih test would the result e etter ompred with the lss verge? 7 Mthletis Instnt Workooks Series K Copyright P Lerning 7

10 Topi 8 - Mesures of spred, interqurtile rnge QUESTION For the following set of sores,,,,, 0,,,, find: the st qurtile (Q) the nd qurtile (Q) (the medin) the rd qurtile (Q) d the interqurtile rnge QUESTION Complete the umultive frequeny tle nd drw umultive frequeny histogrm from the ompleted tle. Sore Frequeny Cumultive frequeny From the grph find: the medin _ the lower qurtile _ the 80th perentile _ d the interqurtile rnge _ e the mode _ QUESTION Find the interqurtile rnge of the following sets of sores.,,, 8,, 8 8, 0,, 0,,,,, 0,, 0,, 0,,,,,, 0, 8 Mthletis Instnt Workooks Series K Copyright P Lerning 8

11 Topi Test PART A Instrutions This prt onsists of 0 multiple-hoie questions Eh question is worth mrk Attempt ALL questions Clultors re NOT to e used Fill in only ONE CIRCLE for eh question Time llowed: 5 minutes Totl mrks = 0 Mrks From pk of 5 rds, one rd is drwn t rndom. Find the proility of drwing dimond. A B C D In single throw of one die, find the proility of throwing n odd numer. A B C D In single throw of two die, find the proility of throwing doule. A B C D For the set of sores, 8,,,, find the rnge. A B 7 C 8 D 9 5 For the set of sores, 0, 0, 50, 0, 0, wht is the differene etween the men nd the mode? A 0 B 0 C 0 D 0 The test mrks of 0 students re, 8, 7. Wht is the modl mrk? A B 7 C 8 D 9 7 For the following set of sores,,,,,,,, the mode is A B.58 C 5 D 8 Find the rnge of the set of sores 8,,, 8,, 9. A 7 B 9 C D 8 9 The medin of the numers,,,, 8, is A 8 B C 5 D 0 The men of the numers 8, 0 nd x is the sme s the men of the numers, 8, 0 nd. Find the vlue of x. A B 9 C 0 D Mthletis Instnt Workooks Series K Copyright P Lerning Totl mrks hieved for PART A 0 9

12 Topi Test Instrutions This prt onsists of 5 questions Eh question is worth mrk Attempt ALL questions Clultors my e used PART B Time llowed: 0 minutes Totl mrks = 5 Questions Answers only Mrks A g ontins yellow, lue nd white lls. If ll is drwn t rndom, find the proility tht it is: TOPIC yellow. TEST SECTION TOPIC lue. TEST SECTION Proility Proility nd nd sttistis TOPIC not white. TEST SECTION Instrutions Proility Proility A oin is tossed for three SECTION nd times the You nd results hve noted. 5 sttistis minutes Use to tree nswer Setion TOPIC TEST SECTION digrm to find the proility of: Eh question worth mrk Instrutions Proility Proility for SECTION nd Attempt You nd hve ALL 5 sttistis questions minutes to nswer Setion TOPIC TEST three tils. Clultors Eh question re NOT worth to e mrk SECTION used Instrutions Proility Proility for SECTION nd Fill Attempt You nd in hve only ALL 5 sttistis ONE questions minutes CIRCLE to nswer for eh Setion question TOPIC TEST 5 two tils nd one hed in ny Clultors Eh order. question re NOT worth to e mrk SECTION used Proility Instrutions Proility for SECTION nd Fill Attempt You nd in hve only ALL 5 sttistis ONE questions minutes CIRCLE to nswer for eh Setion question t lest one til. Clultors Eh question re NOT worth to e mrk used Mrks Instrutions Proility From Proility pk for SECTION of 5 rds, nd one rd Fill You Attempt nd in hve only drwn ALL 5 sttistis ONE questions minutes CIRCLE rndom. to nswer for Find eh Setion the question proility of TOPIC A pir drwing of die TEST is rolled dimond. simultneously. Eh Clultors Find question the re proility is NOT worth to e of mrk used getting: SECTION Mrks Instrutions From pk for SECTION of 5 rds, one rd Attempt Fill You in hve is only drwn ALL 5 ONE questions minutes t CIRCLE rndom. 7 A doule five. B C to nswer for Find eh Setion the question proility D of TOPIC drwing TEST dimond. Clultors Eh question re NOT worth to e mrk used SECTION Mrks Proility From 8 ny doule. Proility pk of 5 rds, nd one rd Fill Attempt nd in only drwn ALL sttistis ONE questions CIRCLE rndom. In A single throw of one B die, find the proility C for Find eh the question proility of throwing n D odd of TOPIC drwing dimond. numer. TEST Clultors re NOT to e used SECTION Mrks Instrutions Proility From 9 sore greter thn 9. Proility pk of 5 rds, for SECTION nd one rd Fill In A single throw of one B You nd in only drwn hve 5 sttistis ONE CIRCLE rndom. die, find the proility C for Find eh the question proility of throwing n D odd of minutes to nswer Setion drwing dimond. numer. Mrks From 0 t lest one six on the uppermost fe of die. pk of 5 rds, one two die, rd Eh question drwn worth rndom. mrk find the proility Find the proility of throwing doule. of Instrutions Proility Proility In drwing A for SECTION nd single dimond. throw of one B Attempt You nd hve ALL 5 sttistis questions minutes die, find the proility C to nswer Setion of throwing n D odd numer. Mrks From the sum of the two numers rolled eing. pk of 5 rds, one two die, rd Clultors Eh is question drwn re is t NOT worth rndom. A B find the C to e mrk used Find the proility of D doule. of Instrutions Fill in only ONE CIRCLE for eh question In drwing for single dimond. SECTION Attempt You hve ALL 5 questions minutes to nswer Setion throw of one die, two even find the proility numers. of throwing n odd numer. For In the single set throw of sores, of two one die, 8, die, Clultors Eh question re is NOT worth, A B find, find the, the proility find C the to e mrk used Fill Attempt in only ALL ONE questions CIRCLE for eh question of rnge. of throwing n D doule. odd numer. Use your lultor to find the men nd stndrd devition, orret For Ato the one set deiml of sores, ple, B 8, for 7 Clultors re NOT, the, following, find sets C the of 8 to e used rnge. sores. D 9 Mrks From pk of 5 rds, one rd is drwn t rndom. Find the proility of drwing In single dimond. throw of two one die, die, find Fill in find the only the proility ONE CIRCLE of of throwing for eh question n doule. odd numer. 5 8,,, 0, 0, 7 50, 0, 0, wht is 8the differene etween 9 the men nd For In A the single set throw of sores, of two B 8, die,,, find, the proility find C the rnge. of throwing D doule. Mrks From pk of 5 rds, one rd is drwn t rndom. Find the proility of drwing the mode? 5,, dimond.,, 0, 0, 7 50, 0, 0, wht is 8the Mrks From pk of 5 rds, one rd is drwn t rndom. differene etween 9 the men nd In For In the the single single mode? 0 set throw throw of sores, of of one two 8, die, die, A B, 0, find find the, the proility proility find C the 0 Find the proility rnge. of of throwing throwing n D doule. odd 0 of drwing dimond. numer. 5 5 For the,, set 5, of sores,,, 0,, 0, 5 50, 0, 0, wht is the differene etween the men nd The For the the mode? test set 0 mrks of sores, of 0 students 8,,, 7 0 re, find, the 8 0 8, rnge. 7. Wht 9 is the 0 In A single throw of one B die, find the proility C of throwing n D odd modl numer. mrk? The test mrks of 0 students 7 re, 8 8, 7. Wht is the 9 5 For the set of sores, 0, 0, 50, 0, 0, wht is the differene etween the men nd modl mrk? For the In A the mode? single 0 set throw of sores, of two one B 8, die, die,, 0, find the, the proility find C the 0 rnge. of of throwing n D doule. odd 0 numer. 7 5 For For The the the test following set of sores, mrks of 0 set 0, students of sores, 0, 50, 0, re,, 0,, wht, is, the, 8,, differene, 7. Wht etween the is mode the the modl is men nd mrk? the mode? In A single throw of two B die, find the proility C of throwing D doule. 75 For the following set of sores, set 0, of sores, 0,.58 50, 0, 7,, 0,, wht, is 5the 8,, differene, etween the mode the 9 is men nd For The the test 0 set mrks of sores, of 0 students 8, 0,, re, find, the 08, rnge. 7. Wht Totl mrks is the hieved 0modl mrk? the In A mode? single throw of two B die, find the proility C of throwing D doule. for PART B 78 Find For the the following rnge of the set of set sores, of.58 sores,, 8,,,,,, 8,,, the 9. mode is 5 The test mrks of 0 students 7 re, 8 8, 7. Wht is the 9 modl mrk? For A the 0 set of sores, B 8, 0,,, find C the 0 rnge. D 0 8 Find 7the rnge of the set of 9 sores 8, Proility, nd, sttistis 8,, For The the test set following mrks of sores, of 0 set students 0, of sores, 0 Mthletis 0, 50, Instnt re 0,,, Workooks 0,, wht,, Series is the, 8,, K differene, Copyright 7. Wht P etween the Lerning is mode the modl the is men mrk? nd A B 7 C 8 D 9 9 The For the medin set of 7 of sores, the numers 8,,, 9,,,, find 8, the is rnge Find the mode? the following rnge of the set of set sores, of.58 sores,, 8,,,,,, 8,,, the 9. mode is 5 For the set of sores, 0, 0, 50, 0, 0, wht is the differene etween the men nd 9 The A medin 8 70 of the numers B 7 90,,, C 8, is 8 0 D Find 7 For the A mode? the following rnge of the set Bof set sores, of.58 sores,, 8,,,, C,, 8,,, the D9. mode is

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