Answer: Find the cumulative probability for 8 in a binomial distribution with n = 20 and p = 0.5.

## Explanation This is a **binomial probability** problem because: - There are a fixed number of trials (n = 20 questions) - Each trial has only two possible outcomes (correct or incorrect) - The probability of success (correct answer) is constant (p = 0.5 for random guessing) - The trials are independent **Key concepts:** - **Option A** finds P(X = 8), which is the probability of getting exactly 8 correct answers - **Option D** finds P(X ≤ 8), which is the cumulative probability of getting 8 or fewer correct answers - The question asks for "8 or fewer" answers correct, which requires cumulative probability **Correct approach:** - Use binomial distribution with n = 20, p = 0.5 - Calculate P(X ≤ 8) = P(X = 0) + P(X = 1) + ... + P(X = 8) - This can be computed using binomial cumulative distribution function (CDF) **Why other options are incorrect:** - **Option B**: Uniform distribution is inappropriate for this discrete probability scenario - **Option C**: Normal approximation might be used, but it's not exact and the question asks for the proper method **Mathematical formula:** P(X ≤ 8) = ∑[k=0 to 8] C(20,k) × (0.5)^k × (0.5)^(20-k) Where C(20,k) is the binomial coefficient "20 choose k".

Author: LeetQuiz .