1. **Problem statement:** There are 50 students in a class, and the professor chooses 15 students at random. We want to find the probability that you or your friend (or both) are among the chosen students. 2. **Understanding the problem:** We want the probability that at least one of the two specific students (you and your friend) is chosen in the group of 15. 3. **Formula and approach:** The total number of ways to choose 15 students from 50 is given by the combination: $$\binom{50}{15}$$ The event "you or your friend (or both) are chosen" is the complement of the event "neither you nor your friend is chosen." 4. **Calculate the complement:** If neither you nor your friend is chosen, then all 15 students are chosen from the remaining 48 students. Number of ways to choose 15 students excluding you and your friend: $$\binom{48}{15}$$ 5. **Calculate the probability of the complement event:** $$P(\text{neither chosen}) = \frac{\binom{48}{15}}{\binom{50}{15}}$$ 6. **Calculate the desired probability:** $$P(\text{you or your friend or both}) = 1 - P(\text{neither chosen}) = 1 - \frac{\binom{48}{15}}{\binom{50}{15}}$$ 7. **Interpretation:** This formula gives the probability that at least one of the two students is in the chosen group of 15. **Final answer:** $$\boxed{1 - \frac{\binom{48}{15}}{\binom{50}{15}}}$$