week2 - !"#$%&'()%*+,-.-/0/12/3%45.061/1% 78'78(9%

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!"#$ &’() *+,-.-/0/12/3 45.061/1 78’78(9 :;;< ’ & !"#$ &’() *+,-.-/0/12/3 45.061/1 :;;< ’ =;32>+;1 ?@A *+,BC D,11 "E.3E2;+ :;;< & !"#$ &’() *+,-.-/0/12/3 45.061/1 & !"#$ &’() *+,-.-/0/12/3 45.061/1 =;32>+; ? $F.GH0;1 I/2E $J>.006 =/<;06 K>23,G;1 :;;< & !"#$ &’() *+,-.-/0/12/3 45.061/1 $F.GH0;1 I/2E $J>.006 =/<;06 K>23,G;1 L,M.6 N>;12/,51 =,21 ,B $F.GH0;1 O,G;I,+< P>; 42 "2.+2 ,B L,M.6Q1 R0.11 D;.M/5S1T 12.+2 3E.H2;+ U /5 D,11 O.5M,>2T LE;1; V,2;1 :;;< & !"#$ &’() *+,-.-/0/12/3 45.061/1 U $J>.006 =/<;06 K>23,G;1 "6GG;2+6 /1 .5 411>GH2/,5 ",G;2/G;1 +;.0/12/3 ",G;2/G;1 >5+;.0/12/3WH/S1) 5>21) -.001) I;.2E;+ LE;+; .+; 5, ,-X;32/Y; H+,-.-/0/2/;1 LE;+; 3.5 -; 3,51;51>1 ,5;1) IE;5 16GG;2+6 /1 +;.0/12/3 ZB I; -;0/;Y; 2E.2 .00 ,>23,G;1 .+; ;J>.006 0/<;06 $F.GH0; ’C[.\) D,00 *./+ ,B P/3; *]">G ^ _‘ ^ *]a&)Ab c C C C c aA)&b‘ ^ A8UA *]">G ^ [‘ ^ *]a&)?b c C C C c a?)&b‘ ^ ?8UA :;;< & !"#$ &’() *+,-.-/0/12/3 45.061/1 ? P { E | S } = #( E ) S ) $F.GH0; ’C[-) U -.001 M+.I5 B+,G c+5 I/2E A IE/2; .5M [ -0.3< -.001 *] & IE/2;) ’ -0.3< -.001 M+.I5 ‘ ^ d K+M;+;M ea"b ^ a&&ba&(ba7b ^ 77( ea$b ^ aAba[ba?b f a[baAba?b f a[ba?baAb ^ Ua&’(b ^ UA( *a & IE/2;) ’ -0.3< ‘ ^ UA(877( ^ ?8&& c5,+M;+;M *a & IE/2;) ’ -0.3< ‘ ^ A(8&A[ ^ ?8&& :;;< & !"#$ &’() *+,-.-/0/12/3 45.061/1 [ S ) = 11 3 " # $ % & = 990 3! = 165; E ) = 6 1 " # $ % & 5 2 " # $ % & = 6(10) = 60 $F.GH0; ’C[3 R,GG/22;; ,B [ M+.I5 B+,G A G;5 .5M 7 I,G;5 411>G; 2E.2 .00 H,11/-0; 3,GG/22;;1 .+; ;J>.006 0/<;06 *] U G;5 .5M ’ I,G;5 ‘ ^ d :;;< & !"#$ &’() *+,-.-/0/12/3 45.061/1 A E ) S ) = 6 3 " # $ % & 9 2 " # $ % & 15 5 " # $ % &
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!"#$ &’() *+,-.-/0/12/3 45.061/1 78’78(9 :;;< ’ $F.GH0; ’C[M) c+5 I/2E 5 -.001 /530>M/5S . 1H;3/.0 ,5; g.001 M+.I5 I/2E,>2 +;H0.3;G;52) ;J 0/<;06 $ ^ ] "H;3/.0 ,5; I/00 -; .G,5S B/+12 < M+.I5 ‘ 402;+5.2; 4HH+,.3E =;2 4/ ^ /2E -.00 M+.I5 /1 1H;3/.0 4&) h ) 45 G>2>.006 ;F30>1/Y;) 3,00;32/Y;06 ;FE.>12/Y; *] 4& c C C C c 4< ‘ ^ < *]4/‘ ^ < a&85b ^ <85 :;;< & !"#$ &’() *+,-.-/0/12/3 45.061/1 _ #( E ) = 1 1 " # $ % & n ( 1 k ( 1 " # $ % & ; S ) = n k " # $ % & P { E } = 1 1 " # $ % & n ( 1 k ( 1 " # $ % & n k " # $ % & = ( n ( 1)! k !( n ( k )! ( k ( 1)!( n ( k )! n ! = k n $F.GH0; ’C[;\) c+5 I/2E -.001 ,B + M/BB;+;52 3,0,+1 =;2 5/ -; 2E; 5>G-;+ ,B -.001 ,B 3,0,+ / 5 ^ 5& f C C C f 5+ ZB .00 ,+M;+1 B,+ M+.I/5S -.001 I/2E,>2 +;H0.3;G;52 .+; ;J>.006 0/<;06) .5M I; 3.55,2 M/12/5S>/1E -;2I;;5 -.001 ,B 2E; 1.G; 3,0,+) .+; .00 H,11/-0; 3,0,+ ,+M;+1 ;J>.006 0/<;06d @d :;;< & !"#$ &’() *+,-.-/0/12/3 45.061/1 9 $F.GH0; ’C[E) g+/MS; O.5M1 411>G; .00 -+/MS; E.5M1 .+; ;J>.006 0/<;06 ZB $ ^ ]400 1H.M;1 /5 ,5; E.5M‘ ZB k ^ ]K5; .3; /5 ;.3E E.5M‘ :;;< & !"#$ &’() *+,-.-/0/12/3 45.061/1 7 S ) = 52 13,13,13,13 " # $ % & ( 5.36 ) 10 28 E ) = 4 1 " # $ % & 13 13 " # $ % & 39 13,13,13 " # $ % & ( 3.38 ) 10 17 * P { E | S } ( 6.3 ) 10 + 12 F ) = 4! 48 12,12,12,12 " # $ % & ( 5.66 ) 10 27 * P { F | S } ( 0.1055 $F.GH0; ’C[/) g/+2EM.61 411>G; ;.3E ,B 2E; 5 H;,H0; /5 . +,,G .+; ;J>.006 0/<;06 2, -; -,+5 ,5 .56 ,B UA[ M.61 +;S.+M0;11 ,B 2E; ,2E;+1 :E.2 /1 2E; H+,-.-/0/26 2E.2 5, 2I, E.Y; 2E; 1.G; -/+2EM.6d ea"b ^ UA[ 5 ea$b ^ UA[ aUA[@&b C C C aUA[@a5@&bb ^ UA[j 8aUA[@5bj *]$l"‘ ^ (C7’A (C[97 (C?7U (C?U& (C’7? (C&(7 5^&( 5^’( 5^’U 5^’[ 5^U( 5^?( :E6 /1 2E/1 1,d d :;;< & !"#$ &’() *+,-.-/0/12/3 45.061/1 &( $F.GH0; ’C[B8S\) *,<;+ 411>G; .56 [ 3.+M1 ;J>.006 0/<;06 k>00 O,>1;T ’ ,B ,5; +.5<) U ,B .5,2E;+ k0>1E T [ 3.+M1 ,B 1.G; 1>/2 "2+./SE2T [ 3.+M1 /5 1;J>;53; a4) ’) U) ?) [b) C C C ) a&() m) N) n) 4b "2+./SE2 k0>1ET 5,2 3,51/M;+;M .1 12+./SE2 ,+ B0>1E :;;< & !"#$ &’() *+,-.-/0/12/3 45.061/1 && S ) = 52 5 " # $ % & = 2,598,960 #(Full House) = 13 1,1,11 " # $ % & 4 2 " # $ % & 4 3 " # $ % & = (13)(12) 4 2 " # $ % & 4 3 " # $ % & = 3,744 ( P {Full House} ) 0.00144 $F.GH0; ’C[B8S\) *,<;+ a3,52/5>;Mb :;;< & !"#$ &’() *+,-.-/0/12/3 45.061/1 &’ #(Same Suit) = 4 1 " # $ % & 13 5 " # $ % & = 5,148 #(Sequence) = 10 1 " # $ % & 4 1 " # $ % & 5 = 10,240 #(Both) = 4 1 " # $ % & 10 1 " # $ % & = 40 ( P {Straight Flush} = 40 S ) ) 1.5 * 10 + 5 ( P {Flush} = 5,148 + 40 S ) ) 1.98 * 10 + 3 ( P
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week2 - !&quot;#$%&amp;'()%*+,-.-/0/12/3%45.061/1% 78'78(9%

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