o zdarzeniach wiadomo

[tomek205]

O zdarzeniach A i B wiadomo, że \(\displaystyle{ P(A \cup B)=5P(A \cap B)}\) i P(B)= P(A'). Oblicz \(\displaystyle{ P(A\cup B)}\)

[kadiii]

\(\displaystyle{ P(A \cup B)=P(A)+P(B)-P(A \cap B)}\) oraz \(\displaystyle{ P(B)=P(A') \Leftrightarrow P(B)=1-P(A)}\)
mamy więc:
\(\displaystyle{ P(A)+1-P(A)-P(A \cap B)=5(P \cap B)}\)
\(\displaystyle{ 1=6P(A \cap B)}\)
\(\displaystyle{ \frac{5}{6}=5(P \cap B)}\)
\(\displaystyle{ P(A \cup B)= \frac{5}{6}}\)