An unprepared student makes random guesses for the ten true-false questions on a quiz. Find the probability that there is at least one corre answer.

To find the probability that there is at least one correct answer when a student makes random guesses on a ten-question true-false quiz, we can use the complement rule. 1. **Calculate the total number of questions**: There are 10 questions. 2. **Determine the probability of guessing incorrectly on one question**: Since each question has two possible answers (true or false), the probability of guessing incorrectly is \( \frac{1}{2} \). 3. **Calculate the probability of guessing incorrectly on all 10 questions**: The probability of guessing incorrectly on all 10 questions is: \[ P(\text{all incorrect}) = \left(\frac{1}{2}\right)^{10} = \frac{1}{1024} \] 4. **Use the complement rule to find the probability of getting at least one correct answer**: The probability of getting at least one correct answer is: \[ P(\text{at least one correct}) = 1 - P(\text{all incorrect}) = 1 - \frac{1}{1024} \] \[ P(\text{at least one correct}) = 1 - \frac{1}{1024} = \frac{1023}{1024} \] Thus, the probability that the student gets at least one correct answer is \( \frac{1023}{1024} \).