Root 5 splits the binomial support between 2 and 3 not at a rounder number

Let $X_{1}, X_{2}, \dots$ be a sequence of independent and identically distributed random variables having Binomial(3, 1/4) distribution. For j=1,2,…, define $Y_{j} = 1$ if $X_{j} \le \sqrt{5}$, and 0 otherwise. If $(1/n)\sum_{j=1}^n$ $Y_{j}^{2}$ converges almost surely to a constant c as $n \to \infty$, then the value of c equals