Prawdopodobieństwo warunkowe
: 14 gru 2010, o 16:25
Oblicz \(\displaystyle{ P(A)}\) jeśli \(\displaystyle{ P(B)=2P(B'), P(A\B)= \frac{1}{5}}\) oraz \(\displaystyle{ P(A\B')= \frac{3}{5}}\)
\(\displaystyle{ P(B)=\frac{2}{3} \\
P(B')=\frac{1}{3} \\
P(A \setminus B) = \frac{P(A \cap B)}{P(B)} \ \Rightarrow P(A \cap B) = \frac{2}{3} \cdot \frac{1}{5} = \frac{2}{15} \\
P(A \setminus B') = \frac{P(A \cap B')}{P(B')} \ \Rightarrow P(A \cap B') = \frac{1}{3} \cdot \frac{3}{5} = \frac{3}{15} \\
P(A) = P(A \cap B) + P(A \cap B') = \frac{1}{3}}\)