t. \( \begin{array}{l}\text { Multiple-choice questions each have four possible answers ( } \mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d} \text { ), one of which is correct. Assume } \\ \text { that you guess the answers to three such questions. } \\ \mathrm{P}(\mathrm{CWC})=\square \text { (Type an exact answer.) } \\ \text { a. Use the multiplication rule to find } \mathrm{P}(\mathrm{CWC}) \text {, where } \mathrm{C} \text { denotes a correct answer and } W \text { denotes a wrong }\end{array} \)

When guessing the answers to three multiple-choice questions, where each question has one correct answer out of four possible choices, we can calculate the probability of getting exactly one correct answer (CWC - Correct, Wrong, Wrong). The probability of picking the correct answer for one question is \( \frac{1}{4} \), and the probability of picking a wrong answer is \( \frac{3}{4} \). Therefore, the probability of CWC can be calculated as follows: \[ P(\text{CWC}) = P(C) \times P(W) \times P(W) = \left(\frac{1}{4}\right) \times \left(\frac{3}{4}\right) \times \left(\frac{3}{4}\right) = \frac{1}{4} \times \frac{9}{16} = \frac{9}{64} \] This means there is a \( \frac{9}{64} \) chance of getting exactly one correct answer when guessing on three questions. To spice things up, think of every guess as a try at a game show! The thrill of hitting that correct answer once while stumbling on the others can be imagined as scoring a partial win in a trivia contest. Just remember, the more guesses you make, the more chances you have, but luck does play a big part! Isn’t math like unfolding the layers of a fun challenge?