A certain primitive calculator has a limited stack, meaning it can calculate $((1 \times 2) \times (3 \times 4 \times (5 \times (6 \times 7))))$, but cannot calculate $((1 \times 2) \times (3 \times 4 \times (5 \times (6 \times (7 \times 8)))))$, because of the 5th nested parenthesis. In fact, this calculator can evaluate any expression with less than 5 nested parenthesis. Sreenath wants to evaluate a certain expression on this calculator that has $10$ left and $10$ right parenthesis. What is the probability the calculator will not have a “stack overflow” error?