The probability that the student guesses exactly three correctly is 0.2656 (or 26.56%). This can be calculated using the binomial probability formula, which is P(x) = nCx * p^x * (1-p)^(n-x). In this case, n is 5 (the number of questions), x is 3 (the number of correct guesses), p is 0.25 (the probability of a correct answer) and 1-p is 0.75 (the probability of an incorrect answer). Plugging these values into the formula gives us 0.2656.