Question

P(A')=1/3 P(B)=P(A/B)=1/2 OBLICZ P(AuB)

Answer 1

P (A') =1/3

P (B) = P(A/B) =1/2

P (A ∪ B) = ?

P (A ∪ B) = P (A) + P (B) - P (A ∩ B)

P (A ∩ B) = P (A) · P (B)

 

P(A) = 1 - P (A') = 2/3

P (A ∩ B) = 2/3 * 1/2 = 2/6 = 1/3

P (A ∪ B)  = 2/3 + 1/2 - 1/3 = 5/6

 

 

 

 

Answer 2

P ( A' ) = 1/3

więc

P( A) = 1 - P(A' ) = 2/3

P( B) = 1/2

P( A / B ) = 1/2

P( A / B) = P(A n B) / P(A)  => P( A n B) = P( A / B) * P(A)

czyli  P( A n B) = (1/2)* (2/3) = 1/3

czyli

P( A u B) = P(A) + P( B) - P( A n B)

P( A u B) = 2/3 + 1/2  - 1/3 = 4/6 + 3/6 - 2/6 = 5/6

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