I’m also not sure if you’re serious, but if you assign a 50% probability to the relevant question being the one with the correct answer of ‘1/2’ and a 50% probability to the relevant question being the one with the correct answer of ‘1/3’ then ‘5/12’ should maximize your payoff over multiple such cases if you’re well-calibrated.
I’m also not sure if you’re serious, but if you assign a 50% probability to the relevant question being the one with the correct answer of ‘1/2’ and a 50% probability to the relevant question being the one with the correct answer of ‘1/3’ then ‘5/12’ should maximize your payoff over multiple such cases if you’re well-calibrated.