Φύλλο εργασίας Πιθανότητες - Ά Λυκείου

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Transcript of Φύλλο εργασίας Πιθανότητες - Ά Λυκείου

: http://lisari.blogspot.com

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2 ()) . ; ; Venn; ) ; ) ; ) ; ) ; ; )

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1 61. . . . 3 () . ( ) . 3 . . . play offs 3 2 . . {1, 2} . 2. : ) (. , ) ) (. ); 3. ( ) 1

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4. 52 ( ). ) ) ) (5)

5.

= { 10, 11, 12, , 20}.

( ) , .

6. 30 . 2/5 , .

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7 97. 20 , , , ) ) ) 3 xi () 0 1 2 3 i () 5 8 4 3

8. = { N / 1 8} . 2 . f ( x ) = 2x 4x + ,

: : f ( x ) = 0

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9. = { N /12 2011} , : ( 4P ( B) 3)2012

+ ( 4P ( A ) 1)

1976

0

) )

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(A) Venn

Venn

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: http://lisari.blogspot.com ( A B = A B

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)

( ) = () ( )

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( ) = ( ) ( )

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( ( ) ( ) ) = ( ) + ( ) 2 ( )

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( ) = 1 ( )

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( ) = 1 ( )

AB

( ) ()

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: http://lisari.blogspot.com , AB=

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10 1310. 400 . . 340 240 . . . . . 3 . : ( ) 5 . . . . ( 2001)11. . 0,7 0,1. . .

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: http://lisari.blogspot.com . . 0,6 : i. . ii. . ( 2006)

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13. 40% , 30% 10% . . : 1. ; 2. ; 3. ; 4. ; 5. ; 6. ;

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- , , :

= () = 0 () = () + () , {. : : , ,

}

, . , ( ) (). - () , , . 0 1. () , , : 0()1 () , : () () : () () () () (: ( ) min P ( A ) , P ( B )} ) () () () () (: max P ( A ) , P ( B)} ( ) ) ( ) () ( ) ()

{

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1. 2. 3. 4. = = = =

:

: , . 5. = 6. 7. 8. = = =

1. = () 2. = 3. = 4. ( ) ( ) = 5. ( ) ( ) ( ) = 6. ( ) = 7. ( ) = 8. = 9. = 10. = 11. = 12. = 13. =

: , , . 9. () = 10. = 11. = 12. () = 13. ( ) =

( 12, 13 De Morgan)

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14 1514. 140 . 98 56 . : : . : . : . i. , , . ii. , : ) 0.1P()0.4 ) 0P()0.3 ) 0.3P()0.6 .

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4 2 ( ) = ( ) = 7 3) , ) ( I )

3 7

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4) ; ) . ; ) ;

16 1716. = {1, 2,3, 4} = {1, 2,3} (1) = (2) = 2 (3) = 3 (4) . ( ) .

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= {1, 2, 3, 4, 5}. , : 2 = {x / 1 }, x4 B = {x / (x25x)(x1)= 6(x1)}. . () ().

1 , (). 4 1 1 . () = () = , 4 8. () = (X), =.

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18 2018. = {1, 2, 3, 4, 5, 6} . P(1) = P(3) = P(5) = 2P(2) = 4P(4) = 2P(6), : . P(1), P(2), P(3), P(4),P(5), P(6). . , : : .

19. = {1, 2,3, 4,5,6,7,8} ) = {1,3} = {6,7,8}

( ) =

2008 + 3 2 2008 () = . ( ) . 6 6

) = {1, 2,3, 4,5} = {4,5,6,7,8} ( ) =

2008 + 3 2 2008 , ( ) = . 6 6

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2020. = {5,4,3,2,1,0,-1} (1)=(0)=(1)=(2)=2(3)=2(4)=2(5). :

= {1,3, x 2 x 3} , = {2, x +1, 2 x 2 + x 2, 2 x +1} x . . , (1), (0), (1), (2), (3), (4), (5). . x BA={- 1, 3}. . x = 1 :

( ) =

5 7 3 , ( ) = , ( ) = 11 11 11

() ( ). ( 2007)

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