Probabilstic Method

Question

This is a question in the book Probabilistic Method by Noga Alon. The question is from the chapter second moment. Show that there is a positive constant $c$ such that the folowing holds. For any $n$ reals $a_{1}, a_{2},....,a_{n}$ such that $\sum_{i=1}^{i=n} (a_{i})^{2} =1 $ if $b_{1}, b_{2}....b_{n}$ is a $ \{-1,1\} $ random vector obtained by choosing each $b_{i}$ randomly, independently with uniform distribution to be either $-1$ or $1$ then $Pr |\sum_{i=1}^{i=n}b_{i}a_{i}| \leq 1 | \geq c $