To solve this problem, we can use the binomial distribution formula:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
where X is the number of correct answers, and P(X = k) is the probability of getting k correct answers out of 5 questions.
The probability of getting a single question correct by guessing is 1/4, and the probability of getting a single question incorrect is 3/4. Therefore, we can calculate P(X = k) using the binomial probability formula:
P(X = k) = (5 choose k) * (1/4)^k * (3/4)^(5-k)
where (5 choose k) is the binomial coefficient, which represents the number of ways to choose k items out of 5.
Plugging in k = 0, 1, and 2, we get:
P(X = 0) = (5 choose 0) * (1/4)^0 * (3/4)^5 = 243/1024
P(X = 1) = (5 choose 1) * (1/4)^1 * (3/4)^4 = 405/1024
P(X = 2) = (5 choose 2) * (1/4)^2 * (3/4)^3 = 270/1024
Adding these probabilities together, we get:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 918/1024
Simplifying this fraction, we get:
P(X < 3) = 459/512
Therefore, the answer is not one of the choices given.