1. **State the problem:** There are 50 students, and 15 are chosen at random. We want the probability that you or your friend (or both) are chosen. 2. **Formula and rules:** The total number of ways to choose 15 students from 50 is given by the combination formula $$\binom{50}{15}$$. 3. To find the probability that you or your friend or both are chosen, it's easier to use the complement rule: find the probability that neither you nor your friend is chosen, then subtract from 1. 4. The number of students excluding you and your friend is 48. The number of ways to choose 15 students from these 48 (excluding both you and your friend) is $$\binom{48}{15}$$. 5. Therefore, the probability that neither you nor your friend is chosen is $$\frac{\binom{48}{15}}{\binom{50}{15}}$$. 6. The probability that you or your friend or both are chosen is: $$ 1 - \frac{\binom{48}{15}}{\binom{50}{15}} $$ 7. This formula accounts for all cases where at least one of you is chosen. **Final answer:** $$ \boxed{1 - \frac{\binom{48}{15}}{\binom{50}{15}}} $$