Chance. Chance. Curriculum Ready.

Transcription

1 Curriulum Redy

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3 This ooklet is ll out the possiility (or hne) of prtiulr events ourring. Mny different gmes involve hne. ere re just few nd the resons why: Crd gmes Bord gmes Guessing gmes The rds you re delt determine your hne of winning Moves depend on the roll of the die Your hne of guessing right depends on the numer of options you hve List some other gmes/tivities you n think of tht involve hne here: Q For ord gme, plyers spin lue ounter wheel nd red ounter wheel. They then move using the rule: lue wheel vlue - red wheel vlue. The first plyer to ross the finish line wins the gme. One plyer is five spes wy from rossing the finish line. Write down ll the different oloured numer omintions tht will give the plyer result of +5 or more to win the gme. Work through the ook for gret wy to do this 1

4 ow does it work? Lnguge of hne event most likelyrin most likelyshould 1highly unlikely 4951 more thn even hne. ertin even hne.

5 ow does it work? Lnguge of hne 1 d 5 e f g h i j k 7 l m n o p

6 ow does it work? Lnguge of hne d e f g LANGUAGE OF CANCE * LANGUAGE OF CANCE * 4

7 ow does it work? Smple spe = 10 S = { } S = { } Coin 1 ( ) ( ) Coin ( ) ( ) ( ) ( ) ( ) ( ) ` S = {( ) () () ()} S = {() () () ()} 5

8 S= 1 4 SAMPLE ZŽůůŝŶŐ Ă ŶŽƌŵĂů ƐŝdžͲƐŝĚĞĚ ĚŝĐĞ d S= S= DŽǀŝŶŐ ƚśŝɛ ĐĂƌ ŐĞĂƌ ƐƟĐŬ e * S= ^ƉŝŶŶŝŶŐ ƚśŝɛ ƐƉŝŶŶĞƌ WƌĞƐƐŝŶŐ Ă ŬĞLJ ĨƌŽŵ ƚśŝɛ ƐƚĂŶĚĂƌĚ ďƶʃžŷ ŬĞLJƉĂĚ f S= S= ŚŽŽƐŝŶŐ Ă ůğʃğƌ ĨƌŽŵ ƚśğ ǁŽƌĚ DĂƚŚĞŵĂƟĐƐ g S= ďăő ĐŽŶƚĂŝŶŝŶŐ ƚśğ ůğʃğƌ ďůžđŭɛ ŝŷ ƚśğ ƋƵĂŶƟƟĞƐ ƐŚŽǁŶ ŚĞƌĞ h # # 4 # # 1 S= dśğ ŶƵŵďĞƌ ŽĨ ƉŝŶƐ LJŽƵ ĐĂŶ ŬŶŽĐŬͲŽǀĞƌ ŝŷ ŽŶĞ ƚƶƌŷ ĚƵƌŝŶŐ Ă ŐĂŵĞ ŽĨ 10ͲƉŝŶ ďžǁůŝŷő i WƐƐƚ LJŽƵ ŵŝőśƚ ŶŽƚ ŬŶŽĐŬ ŽǀĞƌ ĂŶLJ ƉŝŶƐ S= dśğ ƉŽŝŶƚ ƐĐŽƌĞƐ ƉŽƐƐŝďůĞ ǁŝƚŚ ĞĂĐŚ ĚĂƌƚ ƚśƌžǁŷ Ăƚ ƚśŝɛ ĚĂƌƚ ďžăƌě j **** *** 15 *** 0 **** S= 5 10 P 0... / /. E SP A CE &ůŝđŭŝŷő Ă ůŝőśƚ ƐǁŝƚĐŚ SA M * džɛɛŝŷő Ă ĐŽŝŶ * SPACE tƌŝƚğ ĚŽǁŶ ƚśğ ƐĂŵƉůĞ ƐƉĂĐĞ ĨŽƌ Ăůů ƚśğ ƉŽƐƐŝďůĞ ŽƵƚĐŽŵĞƐ ĨŽƌ ĞĂĐŚ ŽĨ ƚśğɛğ CE LE Smple spe 1 PA S MP L SA ow does it work?

9 ow does it work? Smple spe Swith 4 sided die 1 4 Swith 1 Coin S = S = Friends Logged on S = d Plyer Plyer 1 S = 7

10 ow does it work? Smple spe e Spinner 1 1 Die S = =.../.../0...

11 ow does it work? Eqully likely outomes S = { } ` ` S = {1 1 4} 1 S = { } 6 9

12 ow does it work? Eqully likely outomes d e f S = d e f S = S = S = S = 4 S = g S = 10

13 ow does it work? * EQUALLY LIKELY OUTCOMES * EQUALLY LIKELY OUTCOMES Eqully likely outomes.../.../0... S = {1 4} S = { } S = { } d S = { } e S = { 1 } f S = { 1 } 11

14 ow does it work? experiments The frequeny of the event ( E) Experimentl proility of n event ( E) = The numer of trils ompleted th 10 th 1 + = 15 th NO YES 0 th 5 th 0% % % % % % = = = = %

15 ow does it work? experiments th 10 th NO YES 15 th 0 th 5 th 0% % % % % % % = % d 1

16 ow does it work? experiments th NO YES 10 th 15 th 0 th 5 th 0% % % % % % % = % 5 = % = % + % = % = % ' = % d

17 ow does it work? experiments 5 th 10 th NO YES 15 th 0 th 5 th 0% % % % % % % 1 = % = % = % + % = % 1 = % ' = % 6 15

18 ow does it work? experiments %5%10% 5% %, 5%, %, %, %, 5%, 10%, %, %, 5%, %, 10%, 5%, %, 5%, %, %, %, 5%, %, 10%, %, %, 5%, % 5%, %, 5%, 5%, %, %, 5%, %, %, 5%, 10%, 10%, %, 5%, %, %, %, %, 5%, %, %, %, 10%, %, % % 0 5% 1 10% 6 5% 50 = 5 5% = 5% = 1 50 = 4%

19 ow does it work? experiments 5 P() =

20 Where does it work? Theoretil proility Theoretil proility is the expeted hne of events written s frtions, deimls or perentges. It ompres how mny times prtiulr event n hppen with ll the possile outomes. These terms re used lot in proility Totl fvourle outomes = the numer of outomes mthing the result we re looking for. Totl possile outomes = the totl numer of outomes in the smple spe. Proility of n event = Totl numer of fvourle outomes Totl numer of possile outomes The totl numer of fvourle outomes n never e more thn the totl numer of possile outomes ` The proility of n event n only e ny vlue from 0 to 1. ` Proilities in perentge form n only e ny vlue from 0% to 100%. Find the proility of these events (i) Piking red pple from owl ontining 0 pples (1 red nd green). Proility of piking red pple = Piking t rndom is like drwing from ht or losing your eyes efore piking. The numer of red pples (fvourle outomes) The totl numer of pples (possile outomes) = 1 0 = 5 Simplify frtion So if 5 pples re piked (repling the previous pik eh time), you'd expet to e red. (ii) The proility of rolling 4 on twenty-sided die, s frtion, deiml nd perentge Proility of rolling 4 = = The numer of 4s on the die (fvourle outome) The totl numer of sides on the die (possile outomes) 1 0 ` 1 0 = Frtionl proility = 0.05 = 5% Deiml proility Perentge proility 1

21 Where does it work? Theoretil proility 1 M A D A M I M A D A M = A = D = I = M = A = D = I = M = = = 19

22 Where does it work? Theoretil proility.../.../0... * TEORETICAL PROBABILITY * TEORETICAL PROBABILITY 4 d Die Die d 7 100%. 0

23 Where does it work? Desriing theoretil proility % 10% 0% 0% 40% 50% 60% 70% 0% 90% 100% 50% = = + = 10 = 1 0% % 0% 1

24 Where does it work? Desriing theoretil proility 1 d e * DESCRIBING TEORETICAL PROBABILITY.../.../0...

25 Where does it work? Desriing theoretil proility 50%. 90% 100%. d 4% e 5% f 60% g 7%

26 Where does it work? Limittion of theoretil proility should = = 50 = 44% = = 1 = 50% 4

27 Where does it work? Limittion of theoretil proility 1 4 YES NO LIMITATION OF TEORETICAL PROBABILITY *.../.../0... 5

28 Wht else n you do? Proility nottion P (E)= n (E) n (S) (E) = (n) (E) (n) (S) P ( )= n ( ) n ( ) P ( )= 9 = 1 P ( )= P ( )= n () n () = 1 = 0.5 = 5% 6

29 Wht else n you do? Proility nottion 1 P(E) n (E) = 4, n (S) = 5 n (E) = 4, n (S) = 6 P(E) = P(E) = P(E) n (E) = 4, n (S) = 50 n (E) = 5, n (S) = 7 P(E) = P(E) = n (E) =, n (S) = d n (E) = 1, n (S) = 9 P(E) = P(E) = P(E) n (E) = 1, n (S) = n (E) =, n (S) = 5 P(E) = P(E) = n (E) = 6, n (S) = 4 d n (E) = 5, n (S) = P(E) = P(E) = 4 PROBABILITY NOTATION * PROBABILITY NOTATION * P = n () = = n ().../.../0... = ( n P() 1 n ( ) 5 = ) 10 = % P ( ) n () = = n () = 7

30 Wht else n you do? Proility nottion 5.../.../0... d 6 P =

31 Wht else n you do? Plying rds SUITS SYMBOL CARDS IN EAC SUIT PICTURE CARDS A J Q K 1 A J Q K A J Q K 1 A J Q K A J Q K 1 K Q J A A J Q K 1 K Q J A = 5 P ()= n( ) n( ) = 1 5 = 1 4 P ()= n( ) n( ) = 1 5 = 1 9

32 Wht else n you do? Plying rds *PLAYING CARDS *PLAYING CARDS *PLAYING CARDS 1 P ().../.../0... ' P () P ( ) d P ( ) e P () 0

33 Wht else n you do? Plying rds 1 P () P ( nd ) P () 4 A J Q K.../.../0... A Ae J Q K 1

34 Wht else n you do? Prolems involving hne Type ` S = { } P ()= n( ) n() = 1 4 = 5% P ()= 10-4 = 6 n () = 00 ` P ()= n( ) n() = 6 00 = 1%

35 Wht else n you do? Prolems involving hne 1 Seond person First person n ( ) = PROBLEMS INVOLVING CANCE n () =.../.../0... d P( ) e d f e

36 Wht else n you do? Prolems involving hne = 9 = 7 = # 66 # 4 # 4

37 Wht else n you do? Prolems involving hne 4 For eh move in one prtiulr ord gme, plyers spin lue ounter wheel nd red ounter wheel. They then move using the rule: lue wheel vlue - red wheel vlue. This mens they must move kwrds with negtive nswers. The first plyer to lnd on or ross the finish line wins the gme. Complete the tle to see the smple spe of ll the possile sores. Red spinner Blue - Red Blue spinner One plyer is five spes wy from the finish line. Write down ll the different oloured numer omintions tht will give the plyer result of +5 or more to win the gme. n (spin omintions tht will result in win) = d n (different spin omintions) = e P (spinning winning totl) s perentge to 1 deiml ple= f Desrie the hne of this plyer winning this gme. g Briefly omment on mjor flw in the wy this gme llows plyers to move y ompring the numer of possile forwrd nd kwrd movements. 5

38 Chet Sheet Eqully likely outomes ere is wht you need to rememer from this topi on Smple spe ll S = % 10% 0% 0% 40% 50% 60% 70% 0% 90% 100% experiments nd experimentl proility trils (E)= (E) = = = only 01 0%100% P (E)= n (E) n (S) (E)= (n) (E) (n) (S) 6

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