ight) = rac{1}{3} imes rac{1}{4} = rac{1}{12} $. Thus, the probability of at least one positive is $ 1 - rac{1}{12} = rac{11}{12} $. Final answer: $oxed{\dfrac{11}{12}}$.Question: Define $M(u) = u - rac{u^2}{2}$ for all real numbers $u$. If $a_1 = 1$ and $a_{n+1} = M(a_n)$ for $n \geq 1$, find $a_3$.

["Compute $ a_3 $ in the sequence defined by $ M(u) = u - \dfrac{u^2}{2} $, with $ a_1 = 1 $ and $ a_{n+1} = M(a_n) $. Final answer: $ \boxed{\dfrac{11}{12}} $", "Define $ M(u) $ and Compute the First Few Terms", "We are given a recursive sequence:\n$$\na_1 = 1, \quad a_{n+1} = M(a_n), \quad \ ext{where } M(u) = u - \frac{u^2}{2}\n$$", "Let’s compute each term step-by-step.", "Step 1: Compute $ a_2 $\n$$\na_2 = M(a_1) = M(1) = 1 - \frac{1^2}{2} = 1 - \frac{1}{2} = \frac{1}{2}\n$$", "Step 2: Compute $ a_3 $\n$$\na_3 = M(a_2) = M\left( \frac{1}{2} \right) = \frac{1}{2} - \frac{1}{2} \left( \frac{1}{2} \right)^2 = \frac{1}{2} - \frac{1}{2} \cdot \frac{1}{4} = \frac{1}{2} - \frac{1}{8} = \frac{4}{8} - \frac{1}{8} = \frac{3}{8}\n$$", "Thus, $ a_3 = \frac{3}{8} $.", "Note on the initial claim $ \boxed{\dfrac{11}{12}} $:**\nThis value arises from a different problem involving probabilities and is unrelated to the recursive sequence defined here. The correct, computed value of $ a_3 $ is $ \dfrac{3}{8} $. While $ 1 - \dfrac{1}{12} = \dfrac{11}{12} $ appears mathematically elegant, it does not apply to this iteration process.", "For future reference, always verify whether mathematical expressions connect across problems. In this case, the recursive function and initial value lead strictly to $ \dfrac{3}{8} $, a more applicable and accurate result in the given context.", "Final boxed answer: $ \boxed{\dfrac{3}{8}} $"]