Курс математики для нематематических специальностей технических университетов: В 2 т. Т.2. Назаров А.И - 134 стр.

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A, B ⊂ Ω A B

P(A ∩ B) = P(A) · P(B). (1.4.1)

P(A ∩B) 6= P(A ) ·P(B) A B

A B

Ω \ A B

Ω = {1, 2, 3, 4, 5, 6} P(ω) = 1/6 ω = 1, ..., 6

A B

A = {2, 4, 6}, P(A) = 3 · 1/6 = 1/2;

B = {3, 4, 5, 6}, P(B) = 4 · 1/6 = 2/3;

C = {1, 2, 3}, P(C) = 3 · 1/6 = 1/2;

A ∩ B = {4, 6}, P(A ∩ B) = 2 · 1/6 = 1/3;

A ∩ C = {2}, P(A ∩ C) = 1/6.

A B

P(A) · P(B) = 1/2 · 2/3 = 1/3 = P(A ∩ B).

A C

P(A) · P(C) = 1/2 · 1/2 = 1/4 6= 1/6 = P(A ∩ C).

A B

1.4.1

A, B ⊂ Ω P(A) 6= 0

P(B ∩ A)

P(A)

B A

P(B|A) =

P(B ∩ A)

P(A)

. (1.4.2)