Question

Xét hai biến cố A, B trong Hoạt động 1.

a) Tính P(A), P(B), P(A | B), P(B | A).

b) So sánh P(B | A) và \(\dfrac{P\left(B\right).P\left(A\text{|}B\right)}{P\left(A\right)}\).

Answer 1

a) Ta có: \(P\left( A \right) = \frac{{n\left( A \right)}}{{n\left( \Omega  \right)}} = \frac{8}{{24}} = \frac{1}{3};P\left( B \right) = \frac{{n\left( B \right)}}{{n\left( \Omega  \right)}} = \frac{6}{{24}} = \frac{1}{4}\);

\(P\left( {A|B} \right) = \frac{{n\left( {A \cap B} \right)}}{{n\left( B \right)}} = \frac{2}{6} = \frac{1}{3};P\left( {B|A} \right) = \frac{{n\left( {A \cap B} \right)}}{{n\left( A \right)}} = \frac{2}{8} = \frac{1}{4}\).

b) Ta có: \(\frac{{P\left( B \right).P\left( {A|B} \right)}}{{P\left( A \right)}} = \frac{{\frac{1}{4}.\frac{1}{3}}}{{\frac{1}{3}}} = \frac{1}{4} = P\left( {B|A} \right)\).