91影视

Events A and B are disjoint.

Events A and B has positive probability.

Two events A and B would be independent if following condition holds true,

\(P\left( {A\;and\;B} \right) = P\left( A \right) \times P\left( B \right)\)

The disjoint events never occur at the same time.

If two events A and B are disjoint, then \(P\left( {A\;and\;B} \right) = 0\)

The probability of events A and B being positiveimplies that,

\(\begin{aligned}{l}P\left( A \right) > 0\\P\left( B \right) > 0\end{aligned}\)

It is known that,

\(\begin{aligned}{c}P\left( {A\;{\rm{and}}\;B} \right) = 0\\P\left( A \right) \times P\left( B \right) > 0 \Rightarrow P\left( A \right) \times P\left( B \right) \ne 0\end{aligned}\)

Hence, the two disjoint events A and B with positive probabilities are never independent.