Odpowiedź:
z.3
P(A) = [tex]\frac{8}{12}[/tex] P( B) = [tex]\frac{5}{12}[/tex] P( A ∩ B ) = [tex]\frac{2}{12}[/tex]
P ( A ∪ B ) = [tex]\frac{8}{12}[/tex] + [tex]\frac{5}{12}[/tex] - [tex]\frac{2}{12}[/tex] = [tex]\frac{11}{12}[/tex]
z.4
P ( A ∪ B ) = 1
P (A ' ) = [tex]\frac{1}{4}[/tex] ⇒ P( A) = 1 - P( A ') =1 - [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{4}[/tex] = [tex]\frac{9}{12}[/tex]
P ( B ) = [tex]\frac{7}{12}[/tex]
więc
P( A ∪ B) = P( A) + P( B) - P( A ∩ B)
to P( A ∩ B) = P( A) + P( B ) - P( A ∪ B) = [tex]\frac{9}{12} + \frac{7}{12}[/tex] - 1 = [tex]\frac{4}{12}[/tex] = [tex]\frac{1}{3}[/tex]
P ( A \ B ) = P( A) - P( A ∩ B) = [tex]\frac{9}{12}[/tex] - [tex]\frac{4}{12}[/tex] = [tex]\frac{5}{12}[/tex]
Szczegółowe wyjaśnienie:
