Question

Wiadomo że:

P(A')=3P(A)

P(B)=2P(B')

Oblicz :

Answer 1

P ( A' ) = 3 P(A) 

czyli

1 - P(A) = 3 P(A)

1 = 4 P(A)

 P(A) = 1/4

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P( B ) = 2 P( B ' )

P( B) = 2* [ 1 - P( B) ]

P( B) = 2 - 2 P( B)

3 P( B) = 2

P( B) = 2/3

-----------------

P( A n B) = 0,3 = 3/10

zatem

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

P ( A u B) = 1/4 + 2/3 - 3/10 = 15/60 + 40/60 - 18/60 = 37/60

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Answer 2

P(A)=1-P(A')

P(A)-1=-P(A')

1-P(A)=P(A')

 

1-P(A)=3P(A)

4P(A)=1

P(A)=¼

 

P(B)=1-P(B')

1-P(B')=2P(B')

3P(B')=1

P(B')=⅓

P(B)=1-⅓=⅔