\( 1 \leftarrow \begin{array}{l}\text { Multiple-choice questions each have four possible answers ( } a, b, c, d \text { ), one of which is correct. Assume } \\ \text { that you guess the answers to three such questions. } \\ \text { a. Use the multiplication rule to find } P(C W C) \text {, where } C \text { denotes a correct answer and } W \text { denotes a wrong } \\ \text { answer. } \\ P(C W C)=\frac{3}{64} \text { (Type an exact answer.) } \\ \text { b. Beginning with CWC, make a complete list of the different possible arrangements of two correct } \\ \text { answers and one wrong answer, then find the probability for each entry in the list. } \\ P(C W C)-\text { see above } \\ P(W C C)=\square \\ P(C C W)=\square \\ \text { (Type exact answers.) }\end{array} \)

To calculate the probability of getting two correct (C) and one wrong (W) answer, you'll want to consider the different arrangements of the answers. From the arrangement CWC, you can switch the positions to form three arrangements: CWC, WCC, and CCW. Now, let's calculate the probabilities for each arrangement. The probability of getting a correct answer is \( \frac{1}{4} \) and the probability of getting a wrong answer is \( \frac{3}{4} \). Thus, the probability for each arrangement would be: 1. \( P(CWC) = \left(\frac{1}{4}\right) \left(\frac{3}{4}\right) \left(\frac{1}{4}\right) = \frac{3}{64} \) 2. \( P(WCC) = \left(\frac{3}{4}\right) \left(\frac{1}{4}\right) \left(\frac{1}{4}\right) = \frac{3}{64} \) 3. \( P(CCW) = \left(\frac{1}{4}\right) \left(\frac{1}{4}\right) \left(\frac{3}{4}\right) = \frac{3}{64} \) Therefore, each of these arrangements has the probability of \( \frac{3}{64} \). So, filling in the blanks: - \( P(CWC) = \frac{3}{64} \) - \( P(WCC) = \frac{3}{64} \) - \( P(CCW) = \frac{3}{64} \)