Question

In a student's random guesses at a 5 question multiple-choice quiz, each question has four choices with only one correct answer. What is the probability that the student gets exactly two questions right out of three? Identify n, p, and q.

Answer 1

The probability that the student gets exactly two questions right out of three is 9/64.

Step-by-step explanation:

To find the probability that the student gets exactly two questions right out of three, we need to use the binomial probability formula. In this case, n (the number of trials) is 3, p (the probability of success) is 1/4, and q (the probability of failure) is 3/4. We can calculate the probability using the formula P(X=k) = C(n, k) * p^k * q^(n-k), where C(n, k) is the combination of n things taken k at a time.

So, the probability of the student getting exactly two questions right out of three is:

P(X=2) = C(3, 2) * (1/4)^2 * (3/4)^(3-2)

= 3 * (1/16) * (3/4)

= 9/64