, , , . . , , , , , . , , , , -, . , , , . , , .
- . , . , . , , - . : ? : , , . - , .
, - .
, , . ( ). , ( , , ).
, , , . , , , , . , ( ), , .
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1. . , . - : , . , , .
(, , ) . , , , , , .
2. . , , .
3. . , .
4. .
5. , .
6. .
. , , , . , , , , .
: , , .
Ω. . , ( -). . 1 . Ω, .1 ( Ω) .
.
, (.2). (.3).
.
.4 5 , () , . 4 , . 5 . + : , , . U : , . . 6 () . : .
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. - . , , , .
. :
(+) = () + () - ().
(/) , (()≠ 0), ()/ ().
,
() = () (/) =() (/).
:
1. (+ѕD)=P(A) (/)+ () (/), ѕD .
2. (A1A2An-1An)= (A1) (A2 /A1) (An /A1A2An-1An).
:
.
.
(A1)(A2/A1)(An/A1A2An-1An) , , A 1, A 2,..., An.
, , , . , . , . . , .
.
1. . , . , ?
=1/5∙1/4∙1/2∙1=1/120.
2. , , ( ). .
. b - , - . : p(b)=3/5, p(a)=2/5.
, . P(aa)=6/20, P(bb)=2/20, P(ab)=6/20, P(ba)=6/20.
. : - ; - .
, , ={bb,aa}; B={ab,ba}.
P(A)=6/20+2/20=2/5, P(B)=6/20+6/20=3/5.
, , .
3. 3 . 2 1 , 3 1 , 2 2 . . , ?
. - - , 1 - 1, 2 - 2, 3 - 3. (1)= (2)= (3)=1/3, (/ 1)=2/3, (/ 2)=3/4, (/ 3)=2/4=1/2.
()= (1) (/ 1)+ (2) (/ 2)+(3) (/ 3). ()=23/36.
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A ( ):
P (H 1), P (H 2),..., P (Hn), A, , , : , .
. (/) , , Hk, . .
4. (): I 30%, II ʗ55% III ʗ15% . , I 5%, II ʗ6%, III ʗ10%. . . , I ?
:
,
1 I ʻ,
2 II ʻ,
III ʻ.
(/1)=0,05; (/2)=0,06; (/3)=0,1; (1)=0,3; (2)=0,55; (3)=0,15. .
(1/)=0,050,3/(0,050,3+0,060,55+0,10,15)≈0,238. .