Question

Luc is playing a trivia game with multiple choice questions. He runs out of time and needs to guess on the last 2 questions. Each question has 4 multiple choice options (1 of which is correct), so Luc has a 1/4 probability of correctly guessing the answer to any given question. What is the probability that Luc guesses both questions correctly (c)?

a) 1/16
b) 1/8
c) 1/16
d) 1/4

Answer 1

The probability that Luc guesses both trivia questions correctly is found by multiplying the individual probabilities of guessing each question correctly, which is (1/4) x (1/4) = 1/16. Therefore, the correct answer is 1/16, matching option c in the question.

Step-by-step explanation:

The question asks for the probability that Luc guesses both trivia questions correctly, where each question has 4 multiple choice options and the probability of correctly guessing a single question is 1/4. To calculate the probability that Luc guesses both questions correctly, we use the product rule of probability. According to the product rule, if two events are independent (the outcome of one does not affect the outcome of the other), then the probability of both events occurring is the product of their individual probabilities. Therefore, the probability that Luc guesses both questions correctly is:

(1/4) × (1/4) = 1/16

Thus, the correct answer to the trivia game question is 1/16, which corresponds to option c.