Final answer:
To find the probability that the student guesses more than 75 percent of the questions correctly, we can use the binomial probability formula.
Step-by-step explanation:
To find the probability that the student guesses more than 75 percent of the questions correctly, we need to determine the number of questions he needs to guess correctly. Since each question has three possible choices, the probability of guessing a question correctly is 1/3. To calculate the probability, we can use the binomial probability formula:
P(X > k) = 1 - P(X <= k)
P(X <= k) = Sum of (n choose x) * (p^x) * ((1-p)^(n-x)) for x from 0 to k
P(X <= k) = Sum of (32 choose x) * (1/3)^x * (2/3)^(32-x) for x from 0 to k, where n = 32 is the number of questions and p = 1/3 is the probability
By calculating this sum for k = 24, 25, ..., 32 and subtracting from 1 to find P(X > k), we can find the probability that the student guesses more than 75 percent of the questions correctly.