1. Problem: A student guesses on a 4-question true/false quiz. Find the probability of exactly 75% correct answers. 2. Formula: Use the binomial probability formula: $$P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$$ where $n=4$, $k$ is the number of correct answers, and $p=\frac{1}{2}$ (probability of guessing correctly). 3. Calculate $k$ for 75% correct: $$k = 0.75 \times 4 = 3$$ 4. Calculate the probability: $$P(X=3) = \binom{4}{3} \left(\frac{1}{2}\right)^3 \left(1-\frac{1}{2}\right)^{4-3}$$ 5. Simplify: $$P(X=3) = 4 \times \frac{1}{8} \times \frac{1}{2} = 4 \times \frac{1}{16} = \frac{4}{16} = \frac{1}{4}$$ Final answer: The probability of exactly 75% correct is $\boxed{\frac{1}{4}}$ or 0.25.