Probability — a strong law limit for an indicator

Let $X_1,X_2,…$ be a sequence of independent and identically distributed random variables having Binomial$\left(3,\tfrac14\right)$ distribution. For $j=1,2,…$, define $Y_j=1$ if $X_j\le\sqrt5$ and $Y_j=0$ otherwise. If $\frac1n\sum_{j=1}^{n}Y_j^2$ converges almost surely to a constant $c$ as $n\to\infty$, then the value of $c$ equals