To find the probability that the next 4 winners will all be seventh grade students according to Mona's model, we first need to determine the probability of a single winner being a seventh grader.
From the given information, we know that twelve of the last sixteen winners have been seventh graders. Thus, the probability \( P \) of a winner being a seventh grader is:
\[ P(\text{seventh grader}) = \frac{12}{16} = \frac{3}{4} \]
Next, we want to find the probability that all of the next 4 winners will be seventh graders. Since the winners are chosen independently, we can raise the probability of a single seventh grader to the power of the number of winners (4):
\[ P(\text{4 seventh graders}) = P(\text{seventh grader})^4 = \left( \frac{3}{4} \right)^4 \]
Now we calculate \( \left( \frac{3}{4} \right)^4 \):
\[ \left( \frac{3}{4} \right)^4 = \frac{3^4}{4^4} = \frac{81}{256} \]
Thus, the probability that the next 4 winners will all be seventh grade students is:
\[ \frac{81}{256} \]
Therefore, the answer is:
\(\frac{81}{256}\)