Vie has chosen a total ratio where blue beads account for \( \frac{3}{10} \) and yellow beads account for \( \frac{1}{10} \). Together, these two ratios add up to:
\[ \frac{3}{10} + \frac{1}{10} = \frac{4}{10} \]
To find the remaining proportion of orange beads, we need to calculate the remaining part of the total ratio, which is 1 (or \( \frac{10}{10} \)):
\[ 1 - \frac{4}{10} = \frac{10}{10} - \frac{4}{10} = \frac{6}{10} \]
Now we simplify \( \frac{6}{10} \):
\[ \frac{6}{10} = \frac{3}{5} \]
Thus, the ratio of orange beads for each bracelet is \( \frac{3}{5} \).
Therefore, the ratio of orange beads is:
\[ \frac{3}{5} \]