Własn. prawd.

[RazzoR]

Niech \(P(A) = 0,6\), \(P(B) = 0,7\) oraz \(P(A \cup B) = 0,8\). Oblicz \(P(A` \cap B`)\), \(P(B \cap A`)\), \(P(B \cup A`)\).

[radagast]

\(P(A' \cap B')=P((A \cup B)')=1-P(A \cup B)=1-0,8=0,2\)
\(P(B \cap A')=P(B \bez (A \cap B)=P(B)-P(A \cap B)=P(B)-(P(A)+P(B)-P(A \cup B))=P(A \cup B)-P(A)=0,8-0,6=0,2\)
\(P(B \cup A')=P(B )+P(A')-P(B \cap A')=0,7+1-0,6-0,2=0,9\)