Let's say you are taking a true or false test and the distribution of true and false answers questions is not necessarily 50/50, say probability of right answer being false is $p$. Is it true if for a fair coin I let a flip of heads means answer true and flip of tails answer false, I always have 50/50 chance of getting answer right.
My reasoning would be probability of getting answer right would be equal to
$$\frac{1}{2}p+\frac{1}{2}(1-p)=\frac{1}{2}$$
Best Answer
Yes, it's right, and here's why it's counter-intuitive (at least, why it seems that way to me).
Since I'd rather not overuse True/False, let's say the questions are a series of $A$ or $B$ choices. The counter-intuitive part is that it doesn't matter how the right answers are distributed among the $A$ or $B$ choices, only the number of choices and that you're equally likely to choose to $A$ as $B$.
Let's take an extreme example: The right answer is always $A$. But you don't know that, so you happily make random guesses. Then, statistically, you expect to get half of the answers right, since you expect to have randomly chosen $A$ half the time.
So, as long as there are two answer choices and you're randomly guessing, you're expected to get half right, however the correct answers are distributed between the $A$ and $B$ choices.