Final answer:
The question pertains to finding the probability of a student guessing more than 75% of the questions correctly on a multiple-choice exam by using the binomial probability formula. The calculation requires summing up probabilities for all successful outcomes from guessing 24 to 32 questions correctly, with each outcome calculated separately.
Step-by-step explanation:
The subject of this question is Mathematics, specifically dealing with the concept of probability. To find the probability that a student guesses more than 75% of the questions correctly on a multiple-choice exam when guessing randomly, we can use the binomial probability formula. The calculation involves finding the probability of the student guessing 24 out of 32 questions correctly (since 75% of 32 is 24), and then adding the probabilities of guessing 25, 26, ..., 32 questions correctly.
To perform this calculation, we would use the formula:
P(X = k) = (n choose k) * (p^k) * ((1-p)^(n-k))
Where:
- n is the number of trials (questions)
- k is the number of successful trials
- p is the probability of success on a single trial (correctly guessing a question)
Considering there are 3 choices for each question, the probability of guessing correctly is 1/3.
The sum of the probabilities from k=24 to k=32 will give the final answer. Without the exact calculations (as they're not provided in the question), I cannot give an exact answer, but the information provided should guide the student to solve the question using a calculator, such as a TI-83 or TI-84 calculator, which has the necessary functionality for calculating binomial probabilities.