472) An unprepared student makes random guess for ten MCQs questions having 4 options, on a quiz. The probability of atleast one correct answer is: a) 0.9990 b) 0.99 c) 1 d) 0.9437

To determine the probability that an unprepared student gets **at least one** correct answer out of ten multiple-choice questions (MCQs), each with 4 options, we can use the complementary probability approach. ### Step-by-Step Calculation: 1. **Probability of Incorrect Answer for One Question:** - Since there are 4 options and only 1 correct answer, the probability of guessing **incorrectly** is: \[ P(\text{Incorrect}) = \frac{3}{4} = 0.75 \] 2. **Probability of Incorrect Answers for All Ten Questions:** - Since each question is independent, the probability of getting all ten answers incorrect is: \[ P(\text{All Incorrect}) = \left(\frac{3}{4}\right)^{10} \approx 0.0563 \] 3. **Probability of At Least One Correct Answer:** - This is the complement of getting all answers incorrect: \[ P(\text{At Least One Correct}) = 1 - P(\text{All Incorrect}) \approx 1 - 0.0563 = 0.9437 \] ### Conclusion: The probability that the student gets **at least one** correct answer out of ten is approximately **0.9437**. **Answer:** d) 0.9437