PROBABILITY AND STATISTICS REFRESHER SET 1.
How many many 11-letter 11-letter coe coe can !e mae mae "rom t#e wor wor $ATHE$AT $ATHE$ATICS% ICS% a. 1&' !. &( c. 11)
. 1&*
&.
How many comm+ttee, comm+ttee, can !e "orme "orme o" ,tent, can !e "orme "orme "rom t#e /ro0 o" ( ,tent,% ,tent,% a. * !. ( c. 1& . &(
.
$r an $r, $r, eta want want to name t#e+r !a!y !a!y eta ,o t#at t#at +t, mono/ram mono/ram 2F+r,t3 2F+r,t3 $+le3 $+le3 La,t +n+t+al,4 w+ll !e +n al0#a!et+cal orer w+t# no letter, re5+re. How many ,c# mono/ram, are 0o,,+!le% a. 6'' !. (&6 c. '' . 16'
(.
F+n t#e t#e ,tanar ,tanar e7+at+ e7+at+on on o" t#e "ollow+ "ollow+n/ n/ +,tr+! +,tr+!t+on t+on8 8 ( a. 1*
6.
!. (
9 c. '
1& . 9
It re"er, re"er, to eac# mem!er mem!er o" t#e 0o0lat+o 0o0lat+on n #a, an e5al l+:ely l+:ely c#ance c#ance o" !e+n/ ,electe ,electe. . T#e mem!er, o" t#e ,am0le are c#o,en +ne0enently o" eac# ot#er. a. con7en n7en+ +enc ence ,am ,am0le 0le !. rano nom ,am ,am0le 0le c. ,trat rat+"+ +"+e ,am0l m0le . cl, cl,t ter ,am ,am0le 0le
SIT;ATION 18 I" two co+n, are to,,e3 *. =. 9.
<#at +, t#e 0ro!a 0ro!a!+l+ !+l+ty ty o!ta+n+ o!ta+n+n/ n/ at lea,t lea,t one one ta+l% ta+l% a. '.6 !. '.=6 c. '.
. '.&6
<#at +, t#e 0ro!a 0ro!a!+l+ !+l+ty ty o!ta+n+ o!ta+n+n/ n/ at mo,t mo,t one #ea% #ea% a. '.6 !. '.=6 c. '.
. '.&6
How many many !+,#o0, !+,#o0, can one 0t on a ,tan ,tanar ar c#e,,!o c#e,,!oar ar ,c# ,c# t#at no two !+,#o0, !+,#o0, can can #+t eac# ot#er% a. *( !. & c. 1( . =
SIT;ATION &8 Two +ce are t#rown ,+mltaneo,ly. >.
F+n t#e t#e 0ro!a!+ 0ro!a!+l+ty l+ty t#at t#at t#e t#e nm!er nm!er o" ,0ot, ,0ot, 00ermo 00ermo,t ,t +, (. a. 1?1& !. &? c. 1?(
. (?>
1'. F+n t#e 0ro!a!+l+ty 0ro!a!+l+ty t#at t#e nm!er nm!er o" ,0ot, 00ermo,t 00ermo,t +, > or more. a. &? !. 6?19 c. =?* . 9?> 11. F+n t#e 0ro!a!+l+ty 0ro!a!+l+ty t#at t#e nm!er nm!er o" ,0ot, 00ermo,t 00ermo,t +, e+t#er = or 11. a. 1?> !3 &? c. ?( . &?> 1&. Ta!le Ta!le ,#ow, ,#ow, #ow 1' ,tent, ,tent, arran/e arran/e +n al0#a!et al0#a!et+cal +cal orer were ran:e accor+n/ accor+n/ to t#e+r t#e+r ac#+e7ement, on !ot# la!oratory an lectre ,ect+on, o" Sr7ey+n/ cor,e. F+n t#e coe""+c+ent o" ran: correlat+on.
H+nt 8 S0earman@, correlat+on coe""+c+ent +, /+7en !y
a. '.=9&&
!. '.91'>
c. '.96(6
1. F+n t#e ran/e ran/e o" t#+, ,et8 ,et8 1&3*3=331631'31936 1&3*3=331631'31936. . a. 1& !. & c. 16
. '.>&= . =
1(. T#e !oat tra7el, &6 :m. :m. at &6 :0#3 at 6' :0#3 an =6 :0#. F+n t#e #armon+c #armon+c mean o" t#e t#ree 7eloc+t+e,.
a. 6' :0#
!. ('.>
c. &6
. 1.&
SIT;ATION 8 Determ+ne t#e "ollow+n/ 0ro!a!+l+ty 0ro!lem,. 16. A :+n/3 ace3 ac: o" cl!,3 or 5een o" +amon, a00ear, +n raw+n/ a ,+n/le car "rom a well ,#""le or+nary or ec: o" car,. a. 6?&* !. =?9 c. '.>9 . &?> 1*. A non-e"ect+7e !olt w+ll !e "on +" or *'' !olt,3 1& are e"ect+7e. a. 6?&* !. =?9 c. '.>9 . &?> 1=. At lea,t one #ea a00ear, +n t#ree to,,e, o" a "a+r co+n. a. 6?&* !. =?9 c. '.>9
. &?>
19. A !a/ conta+n, w#+te an 6 !lac: !all,. I" two !all, are rawn +n re0lacement3 w#at +, t#e 0ro!a!+l+ty t#at !ot# !all, are !lac:% a. 6?1( !. 1'?1( c. &6?1>* . &6?*( 1>. A cla,,room +n a re7+ew center conta+n, =1 ,tent,3 1' o" t#em are a0am0an/an,3 &( are Bla:enyo, an = are $an+leno,. I" t#ree ,tent, are ranomly a,:e to /et ot o" t#e room3 one a"ter one anot#er3 w#at +, t#e 0ro!a!+l+ty t#at all ,tent, are a0am0an/an,% a. '.''*( !. '.''= c. '.''&1 . '.'''9 &'. T#e nm!er o" e7ent, a,,oc+ate w+t# a ,am0le ,0ace #a7+n/ n otcome, +,8 a. n) !. n c.&n . n& &1. Data wa, collecte a!ot "or ty0e o" r/ e0enent, w#o were :+lle +n o0erat+on to:#an/. T#e nm!er o" re0orte !y PNP +, +,0laye !elow8 Dr/ De0enent, ;,er,?P,#er, Dealer, w+t# Cr+me, ot#er Ca,e,
Fre5ency ' &6 = 6
<#at +, t#e 0ro!a!+l+ty t#at one o" t#e recore :+ll, +, a 0,#er% a. &6?== !.'?*= c. ('?61 . 9?9& &&. A re,tarant +, /+7+n/ away +""erent toy, w+t# eac# c#+l@, meal. <#at +, t#e 0ro!a!+l+ty o" /ett+n/ all t#ree toy, w#en 0rc#a,+n/ 6 meal,% a. '.*1= !. '.9&'( c. '.=>1* . '.6=1 &. I" t#e ,tanar e7+at+on o" t#e mean "or t#e ,am0l+n/ +,tr+!t+on o" ranom ,am0le, o" ,+e * "rom a lar/e or +n"+n+te 0o0lat+on +, &3 #ow lar/e m,t t#e ,+e o" t#e ,am0le !ecome +" t#e ,tanar e7+at+on +, to !e rece to 1.&% a. 16' !. 11' c. 1'' . >* &(. A ,#el" conta+n, t+m!er !oo:,3 ( ,teel !oo:,3 an 6 concrete !oo:,. In #ow many +""erent orer, can t#ey !e arran/e +" all !oo:, o" t#e ,ame color m,t !e :e0t% a. 11&3=>> !. 1'3*9' c. 1(*3&66 . 191=*1 SIT;ATION (8 A ,tent ta:+n/ a tre-"al,e te,t con,+,t+n/ o" 1' 5e,t+on, /e,,e, at t#e an,wer,. A,,m+n/ t#at #e +, e5ally l+:ely to ma:e a correct or +ncorrect /e,, on t#e an,wer,3 &6. F+n t#e 0ro!a!+l+ty t#at #e w+ll /et a 0er"ect ,core. a. 1?&=*9 !. *(6?&=*9 c. 16?&=*9
. 1'?&=*9
&*. F+n t#e 0ro!a!+l+ty t#at #e w+ll /et 9 correct an,wer,. a. 1?&=*9 !. *(6?&=*9 c. 16?&=*9
. 1'?&=*9
&=. F+n t#e 0ro!a!+l+ty t#at #e w+ll /et > correct an,wer,. a. 1?&=*9 !. *(6?&=*9 c. 16?&=*9
. 1'?&=*9
&9. In l+"et+me3 +n wee:,3 o" a certa+n ty0e o" tran,+,tor +, :nown to "ollow a /amma +,tr+!t+on w+t# mean 1' wee:, an ,tanar e7+at+on o" 6' wee:,. <#at +, t#e 0ro!a!+l+ty t#at t#e tran,+,tor w+ll la,t +, at mo,t 6' wee:,% ;,e /amma +,tr+!t+on o" 0ro!a!+l+ty. H+nt8
a. '.>&(6
!. '.>>>6
c. '.>9&*
. '.>=*
&>. a#w+ Leonar3 NBA@, !e,t e"en,+7e 0ro,0ect, a7era/e, & ,teal, 0er /ame. <#at +, t#e 0ro!a!+l+ty t#at #e w+ll #a7e ( ,teal, +n t#e net /ame 7er,, t#e Cl+00er,% ;,e Po+,,on@, 0ro!a!+l+ty +,tr+!t+on. a. '.'9>( !. '.1'1' c. '.1&** . '.1(&> '. G+7en t#e "re5ency +,tr+!t+on !elow3 calclate P ,! 1'. Score, +n Stat+c, Cla,, Inter7al *'-*& 6=-6> 6(-6* 61-6 (9-6' (6-(= (&-(( >-(1 *-9 -6 N a. 9.(
!. (1.6
Fre5ency & & ( 6 11 9 ( & 1 1 ('
c. ((.=
. (9.*
1. In te,t+n/ #y0ot#e,+,3 t#e ma+mm 0ro!a!+l+ty w+t# w#+c# we wol !e w+ll+n/ to r+,: a Ty0e I error +, calle8 a. Dec+,+on Rle, !. S+/n+"+cance Le7el c. Normal D+,tr+!t+on . Error, &. I" a man 0rc#a,e, a ra""le t+c:et3 #e can w+n a "+r,t 0r+e o" P 6''' or a ,econ 0r+e o" P &''' w+t# 0ro!a!+l+t+e, o" '.''1 an '.'' re,0ect+7ely. <#at ,#ol !e a "a+r 0r+ce to 0ay t#e t+c:et% a. P &' !. P 16 c. P 11 . P 1' . F+n t#e 7ar+ance o" t#e "ollow+n/ nm!er,8 -1(3-(3-1'3-1&363-1. a. (=.9( !. (*.6> c. (6.'&
. ((.
(. DeAnre oran +m0ro7e #+, "ree t#row ,#oot+n/ t#at #e a7era/e, ='. <#at +, t#e 0ro!a!+l+ty t#at #e w+ll #+t t#e r "ree t#row on t#e "+"t# attem0t% a. '.196& !. '.'9= c. '.&*(* . '.'=>( 6. Tele0#one nm!er, +n t#e 0ro7+nce ,tart w+t# (61. I" t#e en an !e/+nn+n/ o" t#e net "or nm!er, cannot !e ero3 #ow many 0o,,+!le nm!er, can !e "orme% a. =&>' !. *6*1 c. 1'''' . *6*1 *. A certa+n lotto /ame con,+,t, o" ' +""erent !all,. I" 6 !all, were rawn +n any orer3 #ow many 0o,,+!le com!+nat+on, can !e mae% a. 1(&36'* !. 1(&6*' c. 1=31''3='& . 1=31''3=&' =. How many ( +/+t nm!er, can !e "orme w+t#ot re0eat+n/ any +/+t "rom t#e "ollow+n/ +/+t, 13&33( an *. a. 16' !. 1&' c. 1(' . 1' 9. In a +ce /ame3 one "a+r +, ,e. T#e 0layer w+n, P &' +" #e roll, e+t#er 1 or *. He lo,e, P 1' +" t#e ot#er, trn 0. <#at +, t#e e0ecte w+nn+n/ "or one roll o" t#e +e% a. (' !. ' c. &' . 1' >. A cla,, o" (' too: eam+nat+on +n Hyrolo/y an Tran,0ortat+on En/+neer+n/. I" ' 0a,,e +n Hyrolo/y 3 * 0a,,e +n Tran,0ortat+on En/+neer+n/3 an & "a+le +n !ot# ,!ect,3 t#e nm!er o" ,tent, w#o 0a,,e t#e two ,!ect, +,8
a. &
!. 9
c. &9
. &6
('. How many 0ermtat+on, can !e mae ot o" t#e letter, +n t#e wor ISLAND ta:+n/ "or letter, at a t+me% a. *' !. =&' c. 1&' . &( (1. T#e Cle7elan Ca7al+er, #a, a .=6 w+nn+n/ w#en 0lay+n/ any o" t#e ot#er "or team, +n +t, +7+,+on. I" t#e /ame, are +ne0enent3 w#at +, t#e 0ro!a!+l+ty t#e team cl+nc#e, +7+,+on t+tle a,,me only 1 /ame +, allowe a/a+n,t eac# ot#er% a. '.&1=6 !. '.(&16 c. '.(='* . '.1*( (&. A !alance co+n +, to,,e t#ree t+me,. F+n t#e 0ro!a!+l+ty t#at eactly two o" t#e t#ree w+ll re,lt +n ta+l,. a. 1?( !. ?9 c. ?( . J (. I" 0ro!a!+l+ty A K B K '.16 3 C K '.(3 an D K &E 3 "+n t#e 0ro!a!+l+ty o" D. a. '.& !. '.1 c. '.'6 . '.16 ((. A mac#+ne o0erat+on 0roce, !ear+n/ w+t# +ameter, ,c# t#at are normally +,tr+!te w+t# mean .'''6 +n an ,tanar e7+at+on o" '.''1' +nc#. S0ec+"+cat+on, re5+re !ear+n/ +ameter, to l+e +n t#e +nter7al .''''.''&' +nc#e,. T#o,e ot,+e t#e +nter7al are con,+ere ,cra0 an m,t !e re0a+re. <#at ,#ol t#e mean +ameter +n orer to t#at t#e "ract+on o" !ear+n/, ,cra00e !e m+n+m+e% a. .''1 !. .''6 c. . &.>>6 (6. T#e t+me ta:en !y a term+nal "ee collector to collect term+nal "ee, "rom NAIA #a, an e0onent+al +,tr+!t+on w+t# a mean o" & ,econ,. F+n t#e 0ro!a!+l+ty t#at t#e ranom 0a,,en/er w+ll !e 0roce,,e +n &6 ,econ, or #+/#er% a. '.&>( !. '.= c. '.('6 . '.61> (*. F+n t#e ran/e o" t#e "ollow+n/ ,et o" nm!er,8 16>3&963(>'3>&3=63&>9 a. 1 !. (=6 c. &9> . '1 (=. A !a/ conta+n, &'' mar!le,. T#ere are *' re one,3 *' !le one,3 an t#e rema+n+n/ &' con,+,t o" yellow an w#+te one,. I" mar!le, are c#o,en "rom t#e !a/ w+t#ot loo:+n/3 w#at +, t#e ,malle,t nm!er o" mar!le, one m,t 0+c: +n orer to en,re t#at3 amon/ t#e c#o,en mar!le,3 at lea,t &' are o" t#e ,ame color% H+nt8 ;,e P+/eon#ole Pr+nc+0le. A,,me t#e eac# color #a, 0+c:e one on &' o" t#e ,ame color. a. =6 !. =9 c. 91 . 9( (9. T#e 0ro!a!+l+ty t#at N+cole ,t+e, an 0a,,e, #er De,+/n te,t +, '.(6. I" t#e 0ro!a!+l+ty t#at ,#e ,t+e, +, '.9'3 w#at +, 0ro!a!+l+ty t#at ,#e 0a,,e, De,+/n te,t3 /+7en t#at ,#e #a, ,t+e% a. '.*' !. '.(( c. '.=( . '.6* (>. T#e arran/ement o" ata +n a 0art+clar manner +, calle8 a. O/+7e !. Array c. Fre5ency
. Ran/e
6'. Two rn, conta+n t#e ,ame total nm!er o" !all,3 ,ome !lac:, an ,ome w#+te, +n eac#. From eac# rn are rawn n M !all, w+t# re0lacement. F+n t#e nm!er o" raw+n/, an t#e com0o,+t+on o" t#e two rn, ,o t#at t#e 0ro!a!+l+ty t#at all w#+te !all, are rawn "rom t#e "+r,t rn +, e5al to t#e 0ro!a!+l+ty t#at t#e raw+n/ "rom t#e ,econ +, e+t#er all w#+te, or all !lac:,. ;,e Fermat@, conectre. T#e +m0o,,+!le nm!er o" raw, +, le,, t#an8
a. 16''
!. &'''
c. 6''
. 6''
61. It +, t#e nmer+cal 7ale +n t#e central re/+on o" a +,tr+!t+on o" 7ale,. a. ar+at+on !. Re/re,,+on c. Central Tenency . De7+at+on