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Joined 1 year ago
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Cake day: August 6th, 2023

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  • I see some correct solutions for the 50% case here already, so this reply is going for a perfect score within two tries.

    There are 16 ways to answer the quiz, one of which is correct. Assuming you don’t repeat your previous answers, two attempts give you a 2/16 or 1/8 chance that one of them is perfect.

    Now if you get feedback between your attempts, you should be able to do better. Let’s see by how much and break it into cases:

    1. Your first guess is already perfect. This happens 1/16 of the time. No further guessing is needed.

    2. Your first guess is 50% correct. This happens 3/8 of the time. Picking one of the unguessed answers improves your score to 100% 1/6 of the time.

    3. Your first guess is completely wrong. This happens 9/16 of the time. Picking different answers for both questions wins 1/9 of the time.

    So the overall chance of a perfect score is the weighted sum of these cases or 1/16 + (3/8 * 1/6) + (9/16 * 1/9) = 3/16.