Cho hai biến cố \[A\] và \[B\], với P ( A) = 0,4 , P ( B ) = 0,7

a) Đúng.

Ta có: \[P\left( {\overline A } \right) = 1 - P\left( A \right) = 0,6\]

           \[P\left( B \right) = 1 - P\left( {\overline B } \right) = 0,3\].

b) Sai.

Ta có: \[P\left( {A|B} \right) = \frac{{P\left( {A \cap B} \right)}}{{P\left( B \right)}} = \frac{{0,3}}{{0,7}} = \frac{3}{7}\].

c) Sai.

Ta có: \[P\left( {\overline B |A} \right) = 1 - P\left( {B|A} \right) = \frac{{P\left( {A \cap B} \right)}}{{P\left( A \right)}} = 1 - \frac{{0,3}}{{0,6}} = 0,5\].  

d) Sai.

Ta có: \[P\left( {\overline A  \cap B} \right) = P\left( {\overline A |B} \right).P\left( B \right)\]  

Mà \[P\left( {\overline A |B} \right) = 1 - P\left( {A|B} \right) = \frac{{P\left( {A \cap B} \right)}}{{P\left( B \right)}} = 1 - \frac{{0,3}}{{0,7}} = \frac{4}{7}\]

\[P\left( {\overline B  \cap A} \right) = P\left( {\overline A |B} \right).P\left( B \right) = \frac{4}{7}.0,7 = \frac{2}{5}\].