Final answer:
The probability of guessing more than 75 percent of a 32-question multiple-choice exam correctly when each question has three options is calculated using the binomial probability formula, which is computationally complex and typically requires a calculator or software.
Step-by-step explanation:
Finding the Probability of Correct Guesses
To find the probability that a student guesses more than 75 percent of the questions correctly on a 32-question multiple-choice exam, we calculate the probability of guessing correctly on each question and then use the binomial formula to find the cumulative probability. Since each question has three possible choices, the probability of guessing correctly on a single question is ⅓ (or about 0.333). To guess more than 75 percent of the questions correctly, the student would need to guess at least 24 out of 32 questions correctly.
Using the binomial probability formula:
Identify the probability of success on a single trial, p = 0.333.
Identify the number of trials (n = 32) and the number of successes (x ≥ 24).
Use the formula to calculate the cumulative probability for x ≥ 24 successes.
This calculation is complex and would typically require computational tools such as a binomial probability calculator or statistical software.
It's important to note that the probability of guessing more than 75 percent correctly is extremely low because the likelihood of guessing each individual question correctly is low to begin with. As the number of questions increases, the possibility of achieving this level of accuracy by random guesses decreases exponentially.