Everyone in here is so quick to forget their quant!
Sure you may expect to get 1/3 of those questions right, if you truly randomly guess. But will you really get 1/3 of those questions right?
Without knowing the underlying population and its distribution characteristics, there is no way to tell! The average could most certainly be 1/3, but what about the variance of the distribution? The population could very well have a large variance and standard deviation. Constructing a confidence interval for even 1 standard deviation out from the mean could result in a wide range of possibilities. What about three standard deviations to capture 99.8% of the possibilities? To what p-value can we expect the average to be significantly different from 1/4, 1/10, or even zero?
And that’s if the underlying population distribution is normal. What if your guesses aren’t truly random? Humans are notorious for their quirks that result in biased choices. Oh you’ll randomly guess? Except for this one that you’re kind of sure of, but will most likely get killed by that CFA trap?
I’m f***ing losing it guys.