 .
 


              .      ,         .       .       ,    ,     .





 

 .





:

1) ;   .

2)   .

3) ,    .

4)    .

4. 1    .

4. 2     .

4. 3     .

4. 4  .

4. 5    .

4. 6     .

4. 7    .

5)   .

6)   .

7)   .

8)   .

9)   .

9. 1        .

9. 2        .

10)   ,      .

11)   .

12)     .

13)    .

14)    .



 .

1)) ;   .

1. .

    n   m     ,    ,    ,       n   m .








2. .

    n   m     ,      n   m .








3. .

    n       ,      n .








     .

4.   .

     n   m        ,         n   m .








5.   .

     n   m      ,   ,         n   m .








6.   .

        n ,  k  ,      n1 ,    n2   k -    k ,         n .

Pn (n1, n2,  nk)  = n! / n1! n2!  nk!

2))   .

 -   -   .

          ,     .

    ,      ,     .

    ,       .








    ,        .

   ?

   ,                ().

    ,      ,      .

    ,           .

    ,    ,      ,  .

3)) ,    .

     ,        .








            .








     ,  ,     ,     .

A -  .

B -  .

C = A / B = A - B

  A  B  C.















4))    .

4. 1    .

    ,          .

    ,         .

4. 2     .

           .

 () = m / n

A - .

P (A) -  .

m -   .

n -   .

4. 3     .

       .

          .

P (A1 + A2 +  +  n) = P (A1) + P (A2) +  + P (An)

1, 2,  An -  .

P (1), P (2), P (An) -   .

 1     .

        .

P (A1) + P (A2) +  + P (An) = 1

1, 2,  An -      .

 2     .

      .

 () + P (?) = 1

 - , .

A? -  , .

P (A) -  , .

P (A?) -   , .

4. 4  .

   B   ,   A ,     B.

    P (A / B)  P A (B)

4. 5    .

    ,         .

              ,   ,    .

P (A ? B) = P (A) ? P (B / A)

                .

P (A1 ? A2 ?  ? An) = P (A1) ? P (A2 / A1) ? P (A3 / A2 / A1) ? P (An / A n-1 /  / A1)

 ,        ,     .

4. 6     .

    ,           .

           .

P (A ? B) = P (A) ? P (B)

P (A1 ? A2 ?  ? An) = P (A1) ? P (A2) ?  ? P (An)

4. 7    .

         ,    .

P (A + B) = P (A) + P (B) - P (A ? B)

     ,         .

A1, A2,  An -  .

A?1, A?2,  A?n -   .

P (A1 + A2 +  + An) = 1 - P (A?1 ? A?2 ?  ? A?n)

5))     .

  -  ,    .

1.     .

P (A) ? 0

2.     .








3.         .

P (A1 + A2 +  + An) = P (A1) + P (A2) +  + P (An)

4.   -  .

        .

A1 ? A2 ?  ? An = ?

6))   .

1.        .

P (A?) = 1 - P (A)

2.      .

P (?) = 0

? -  .

3.         .

0 ? P (A) ? 1

4.   A     B,         B.

P (A) ? P (B)








5.              .

P (A + B) = P (A) + P (B) - P (A ? B)

A, B -  .

6.          .

P (A + B) ? P (A) + P (B)

A, B -   .

7.    B   ,          .

P (B / A) = P (A ? B) / P (A)

  P (A) ? 0

7))   .      .

     ,       .

     .

A  B.

.

   H          A1, A2,  An,    ,    H              H.

P (H) = ? P (Ai) ? P (H / Ai)

i -   - .

8))   .

     P()  P (B),    .

    .

  B.

P (H / ) = P (A) ? P (H / A) / P (H)

P (H / B) = P (B) ? P (H / B) / P (H)

P (H) = P (A) ? P (H / A) + P (B) ? P (H / B)

          .

P (H / i) = P (Ai) ? P (H / Ai) / ? P (Ai) ? P (H / Ai)

Ai -       .

9))   .

9. 1        .

 1.

       .

  ,       p1 = 0,1; p2 = 0, 4; p3 = 0, 5 .

  ,           98%;  88%; 92% .

:

p1 = 0, 1

p2 = 0, 4

p3 = 0, 5

q1 = 98% = 0, 98

q2 = 88% = 0, 88

q3 = 92% = 0, 92

:

1.  ,         .

2.        .

:

,           .

       .

0, 1 + 0, 4 + 0, 5 = 1

1 = 1

    . ,    .

     .

P (H) = P (A) ? P (H / A) + P (B) ? P (H / B) + P () ? P (H / )

A, B, C -  ,        .

A -     .

B -     .

C -     .

P (A) -      .

P (B) -      .

P (C) -      .

H - ,      .

P (H) - ,     .

P (H / A) = q1 -  ,        .

P (H / B) = q2 -  ,        .




  .


   .

   ,     (https://www.litres.ru/book/vasilisa-volkonskaya/teoriia-veroiatnostei-74658338/)  .

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