The probability that an event $$A$$ happens in one trial of an experiment is $$0.4.$$ Three independent trials of the experiment are performed. The probability that the event $$A$$ happens at least once is

Two events $$A$$ and $$B$$ have probabilities $$0.25$$ and $$0.50$$ respectively. The probability that both $$A$$ and $$B$$ occur simultaneously is $$0.14$$. Then the probability that neither $$A$$ nor $$B$$ occurs is

The smallest positive integer n for which $${\left( {{{1 + i} \over {1 - i}}} \right)^n} = 1$$ is

Given $$y = {{5x} \over {3\sqrt {{{\left( {1 - x} \right)}^2}} }} + {\cos ^2}\left( {2x + 1} \right)$$; Find $${{dy} \over {dx}}$$.