Talk:Pirate/@comment-25876622-20170601021957/@comment-32132097-20170601101539

$$ P(X>=2)=1-P(X<=1)=1-(B(n;1/3;0)+B(n;1/3;1))=1-(\frac23^n+n*1/3*\frac23^{n-1})=1-\frac23^{n-1}(\frac23+n*1/3)=1-\frac23^{n-1}(\frac23+n/3) $$