Pablo will decorate each of 6 identical white balls with either a striped, dotted, or checkered pattern, using either red or blue paint. He will decide on the color and pattern for each ball by flipping a fair coin for the color and rolling a fair 3-sided die for the pattern for each of the 6 balls. After the paint dries, he will place the 6 balls in an urn. Frida will randomly select one ball from the urn and note its color and pattern. The events "the ball Frida selects is red" and "the ball Frida selects is striped" may or may not be independent, depending on the outcome of Pablo's decisions. The probability that these two events are independent can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m$? (Recall that two events $A$ and $B$ are independent if $P(A\text{ and }B)=P(A)\cdot P(B)$)