Final answer:
To find the probability that a student earns exactly 5 points on both parts of the quiz, we multiply the probabilities of earning 5 points on each part. If each part is scored out of k, the probability is 1/k^2.
Step-by-step explanation:
To find the probability that a student earns exactly 5 points on both parts of the quiz, we need to assume that the points earned on each part of the quiz follow a discrete probability distribution. Let's represent the number of points earned on the first part with random variable X, and the number of points earned on the second part with random variable Y.
Since X and Y are independent random variables, we can find the probability by multiplying the probabilities of earning 5 points on each part. Let p(X=5) be the probability of earning 5 points on the first part, and p(Y=5) be the probability of earning 5 points on the second part. If both parts are scored out of k, and each score from 0 to k is equally likely, then p(X=5) = p(Y=5) = 1/k.
Therefore, the probability of a student earning exactly 5 points on both parts is p(X=5) * p(Y=5) = (1/k) * (1/k) = 1/k^2.