1. **Problem statement:** Calculate the probability that Anna wins two main prizes when she buys 2 tickets from 100 tickets, where 3 are main prizes and 12 are consolation prizes. 2. **Formula used:** The probability of winning two main prizes without replacement is given by the product of probabilities of drawing a main prize on the first draw and then on the second draw: $$P(2\text{ main prizes}) = \frac{3}{100} \times \frac{2}{99}$$ 3. **Explanation:** Since Anna buys 2 tickets without replacement, the total number of tickets decreases by 1 after the first draw. 4. **Calculation:** $$P = \frac{3}{100} \times \frac{2}{99} = \frac{6}{9900}$$ 5. **Simplify the fraction:** $$\frac{6}{9900} = \frac{\cancel{6}^1}{\cancel{9900}^{1650}} = \frac{1}{1650}$$ 6. **Final answer:** The probability that Anna wins two main prizes is $$\boxed{\frac{1}{1650}}$$