The probability that an event does not happen in one trial is 0.8. The probability that the event happen atmost once in three trials is 

Given Probability of not happening of trails =0.8

and Probability of happening of trails =0.2

Probability that event happens at most once in 3 trails 

            =p(0 times)+p(1 times in three trails)

           $$\begin{gathered} =0.8\times 0.8\times 0.8+3(0.2\times 0.8\times 0.8) \\ =0.512+0.384 \\ =0.896 \end{gathered}$$