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

Solution :
$$p = 0.4,n = 3,P\left( {X \geqslant 1} \right) = \,\, ?$$
⇒ $$q$$ = 0.6
$$\eqalign{ & \therefore \,\,P\left( {X \geqslant 1} \right) = 1 - P\left( {X = 0} \right) \cr & \,\,\,\,\, = 1 - {\,^3}{C_0}{\left( {0.4} \right)^0}{\left( {0.6} \right)^3} \cr & \,\,\,\,\, = 1 - 0.216 \cr & \,\,\,\,\, = 0.784 \cr} $$