Question

Find the probability of each event. A test consists of seven true/false questions. A student who forgot to study guesses randomly on every question. What is the probability that the student answers exactly five questions correctly?

a. ( 21/128 )
b. ( 35/128 )
c. ( 7/64 )
d. ( 1/32 )

Answer 1

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).