wrong.
Non arbitrage means that
all self financing portfolio with zero intial cost could not have only postive payoff.
Mathematically,

No such portfolio :  
V_0 = 0 and V_T>=0 and P(V_T>0)>0.

If V_0 =0 and V_T >0 with prob p and V_T<=0 with prob 1-p,  this is not an arbitrage coz you could not make safe money, you will lose with proba 1-p.

wish this would help.