I've been debating this with friends.
I'm beginning to think this is a paradox with no correct answer (?)
Can anyone explain their choice if they have one?
What do the choices A, B, C, and D mean
Possibly
(1)Choice A means your would answer the question correctly 25% of the time, choice B means you would answer the question correctly 50% of the time, etc.
or
(2)Four overlapping choices A, B, C, and D where only one of the choices, i.e. either A [and thus D] is the correct answer to the unknown question but not B and not C, or B is the correct answer to the unknown question but not A [and thus not D] and not C, or , or C is the correct answer to the unknown question but not A [and thus not D] and not B
or
...
In case(1) you have an unusual expected value question. That is each case (A, B, C, and D) has a probability of 25% of being chosen so 'normally' [each choice independent] you would just multiply each case by 0.25 and sum [or sum and multiply by 0.25]. However, in this situation, the choices of A, B, C, and D, are clearly dependent (have overlapping sets) because their sum is greater than 1. So, in order to answer the question, one would need to know how this 'overlap' occurs.
In case (2) go through an 'infinity of trials', you would chose A or D[25%] 50% of the time, choose C 25% of the time, and choose D 25% of the time. If the correct answer were 25%, you would be correct 50% of the time; if the correct answer were 50% you would be correct 25% of the time; if the correct answer were 60% you would be correct 25% of the time. So, in this particular case, the answer needs to be known before you can answer the question.
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