1. **State the problem:** We have a total of $12c + 36$ raffle tickets, and among them, $7c + 21$ are winning tickets. We want to find the probability of picking a winning ticket at random. 2. **Formula for probability:** The probability $P$ of an event is given by $$P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ Here, favorable outcomes are winning tickets, and total outcomes are all tickets. 3. **Apply the formula:** $$P = \frac{7c + 21}{12c + 36}$$ 4. **Simplify the fraction:** Factor numerator and denominator: $$7c + 21 = 7(c + 3)$$ $$12c + 36 = 12(c + 3)$$ 5. **Cancel common factors:** $$P = \frac{7(c + 3)}{12(c + 3)} = \frac{7}{12}$$ 6. **Final answer:** The probability of picking a winning ticket is $$\boxed{\frac{7}{12}}$$ This fraction is already in simplest form.