I know this is an easy problem, but I can't figure it out.

A particle takes discrete steps $σ_1,σ_2,σ_3,…,σ_n$ which take on values +1 or −1. However, $P(σ_i=+1)=p$ and $P(σ_i=−1)$ will be $1-p$.

So I am interested in bound of $ P (\sum_{i}{\sigma_i} \geq k)$ ?

I tried to use Chernoff's bound, but it doesnt give me a good bound. Also for Chernoff I need to have $k \geq \mu$.

Can I say that $\sigma$-s correspond to some other $Y_i$, such that $Y_i = 1$, with prob. $p$ and $0$, with prob $1-p$, and we are interested in

$P(\sum_i{Y_i} \geq k/2)$?