91Ó°ÊÓ

First, let's define the following events:Event A: The first answer is correct.Event B: The second answer is correct.

The probability of getting the first answer correct (Event A) is 1 out of 4 (\( \frac{1}{4} \)) since there's only one correct answer out of 4 options. Same for the second question.So P(A) = P(B) = \( \frac{1}{4} \). P(A and B), meaning the probability that both answers are correct, is simply the product of their individual probabilities (since they are independent events).So P(A and B) = P(A) * P(B) = \( \frac{1}{4} \) * \( \frac{1}{4} \) = \( \frac{1}{16} \).Now, we don't know that exactly one or both questions were answered correctly. Hence, we need to consider P(A or B), which is the probability that either Event A occurs or Event B occurs or both. This is given by P(A) + P(B) - P(A and B).So P(A or B) = P(A) + P(B) - P(A and B) = \( \frac{1}{4} \) + \( \frac{1}{4} \) - \( \frac{1}{16} \) = \( \frac{7}{16} \).

We need to find the conditional probability that both answers are correct (A and B) given that at least one is correct (A or B). This is given by the formula:P(A and B | A or B) = P(A and B) / P(A or B)Substituting the values we calculated in Step 2, we find:P(A and B | A or B) = \( \frac{1}{16} \) / \( \frac{7}{16} \) = \( \frac{1}{7} \)