sequences and series - Show that $Y_n$ converges in probability

I attempted part ii of the question with the following:

To show that $Y_n$ converges in probability, I started off with $P(|Y_n-0|>\epsilon$). I then wrote, for $0<\epsilon<\theta$

$P(Y_n<-\epsilon).$ However, trying to evaulate this lead me nowhere. Upon looking at the solutions:

It says that $P(Y_n>\epsilon)$. Why is this so? How do I know that $Y_n$ is positive?