Final answer:
To find the probability that the student answers exactly five questions correctly, we can use the binomial probability formula.
Step-by-step explanation:
To find the probability that the student answers exactly five questions correctly, we can use the binomial probability formula. The probability of success (answering correctly) is 1/2, since the student is randomly guessing on each question. The probability of failure (answering incorrectly) is also 1/2. We need to calculate the probability of getting exactly 5 successes out of 7 trials, which can be done using the formula:
P(X = k) = (nCk) * p^k * (1-p)^(n-k)
Here, n is the number of trials (7), k is the number of successes (5), p is the probability of success (1/2), and (nCk) is the number of ways to choose k successes out of n trials.
Using this formula, the probability of answering exactly five questions correctly is:
P(X = 5) = (7C5) * (1/2)^5 * (1/2)^(7-5) = 21/128
Therefore, the correct answer is a. (21/128).