SaVe Points: 0 of 1 Each question of a 5 -question multiple choice exam has 5 possible answers. Suppose a student picks an answer at randorh question. Find the probability the student selects the correct answer on none of the questions. The probability that none of the questions are answered correctly is (Simplity your answer. Type an integer or a fraction.)

To find the probability that the student selects the correct answer on none of the questions, we first determine the probability of getting a question wrong. With 5 possible answers for each question, there is 1 correct answer and 4 incorrect answers. Thus, the probability of picking an incorrect answer is: \[ P(\text{incorrect}) = \frac{4}{5} \] Since the student answers all 5 questions and we want the probability of getting all of them wrong, we raise the probability of getting a question wrong to the power of the number of questions: \[ P(\text{none correct}) = \left(\frac{4}{5}\right)^5 \] Calculating this value: \[ P(\text{none correct}) = \frac{4^5}{5^5} = \frac{1024}{3125} \] So, the probability that none of the questions are answered correctly is: \[ \frac{1024}{3125} \]