Wow. I was going to disagree with you... then I read the quiz and note. It's worse than a mere error, the quiz writer is willfully throwing away knowledge about the world.
They didn't give conditional probabilities but of course we can, and should, use what we know about the world to make guesses at P(E|'likes math'), or at least whether that's greater than P(L|'likes math'). It surely is and you can do something similar with carpentry and an apolitical nature.
It's true that even with the assumptions I've given above you can't come up with a precise answer - none of the choices are any good - you can certainly say that "...the correct response being precisely 30 percent" is thoroughly wrong.
They didn't give conditional probabilities but of course we can, and should, use what we know about the world to make guesses at P(E|'likes math'), or at least whether that's greater than P(L|'likes math'). It surely is and you can do something similar with carpentry and an apolitical nature.
It's true that even with the assumptions I've given above you can't come up with a precise answer - none of the choices are any good - you can certainly say that "...the correct response being precisely 30 percent" is thoroughly wrong.