Two urns, $U_1$ and $U_2$, contain colored marbles. $U_1$ holds $3$ red and $2$ blue marbles, while $U_2$ holds $2$ red and $4$ blue marbles. A fair die is rolled; if the result is $1$ or $2$, a marble is drawn from $U_1$. Otherwise, a marble is drawn from $U_2$. If the drawn marble is red, what is the probability it originated from $U_1$?