A quiz has only 1 multiple choice question with answers a, b and c & only 1…

Concept: For two independent trials, the probability that both fail is the product of each trial's own failure probability, P(both fail) = P(fail 1) × P(fail 2). By the complement rule, the probability that at least one succeeds is P(at least one success) = 1 − P(both fail).

Applying this to the quiz:

1. The multiple-choice question offers 3 answer choices (a, b, c), so a random guess is correct with probability 1/3 and incorrect with probability 1 − 1/3 = 2/3.

2. The true/false question offers 2 answer choices, so a random guess is correct with probability 1/2 and incorrect with probability 1 − 1/2 = 1/2.

3. The two guesses are independent, so the probability that BOTH are wrong is 2/3 × 1/2 = 1/3.

4. By the complement rule, the probability of answering at least one question correctly is 1 − 1/3 = 2/3.

Cross-check by direct enumeration: with MCQ-correct probability 1/3 and TF-correct probability 1/2, the four joint outcomes are (both correct) 1/3 × 1/2 = 1/6, (only MCQ correct) 1/3 × 1/2 = 1/6, (only TF correct) 2/3 × 1/2 = 1/3, and (both wrong) 2/3 × 1/2 = 1/3. Summing every outcome with at least one correct answer gives 1/6 + 1/6 + 1/3 = 2/3, confirming the result.

So the probability of answering at least one of the two questions correctly is 2/3.