To answer this question we will use the following expression to compute the probability that an event occurs:
[tex]\frac{FavorableOutcomes}{TotalOutcomes}.[/tex]Since the choice is with replacement, then the probability of choosing a red ball is always the same.
The probability of choosing a red ball is:
[tex]\frac{3}{3+4+7}=\frac{3}{14}.[/tex]Then the probability of choosing 3 red balls is:
[tex]\frac{3}{14}\times\frac{3}{14}\times\frac{3}{14}=\frac{27}{2744}.[/tex]Answer:
[tex]\frac{27}{2744}.[/tex]