Strange logic question, truth of predictions 1: Half of my predictions come true;
2: I predict A;
3: I predict B.
Now, suppose A come true, so that the prediction 2 is true; and B come false.
So, half of my predictions came true and 1 is also true; BUT in this way, 2/3 of my predictions came true so 1 is false. Contradiction??
Maybe it's only a nonsensical mental whimsy of mine.
 A: Consider:
$$\tag{1}\text{Half of my predictions come true.}$$
$$\tag{2}A\text{ is one of my predictions.}$$
$$\tag{3}B\text{ is one of my predictions.}$$
Now; $(1)\iff(2)\land(3)$. You seem to have implied that when $A$ occurs, $B$ cannot occur and vice versa, i.e., that $A$ and $B$ are mutually exclusive. Ergo, $\neg((2)\land (3))$. Thus, $\neg(1)$. Therefore, $(2)\oplus(3)$, $\oplus$ being the XOR or exclusive or operation.

Now, consider this: The OP has said that $(1)$, originally, was not considered a prediction; shortly after arriving at the conclusion that $(1)$ is dependent on $(2)$ and $(3)$, the OP then thought $(1)$ to indeed be a prediction. And thus, the apparent paradox is formed. 
This “paradox” was created by a informal logical fallacy commonly known as equivocation; that is, changing the definition of a world or lexical entry. We know using a fallacy can lead to a very wrong conclusion (e.g. “I am alive”, “the President is alive”, therefore, “I am the president”; syllogistic fallacy of Undistributed Middle).
Though, the way I understand it, the confusion arose from the seemingly-variable state of $(1)$, that, since it refers to itself, must it be true or false?
Perhaps this is an example of Richard's Paradox, found most commonly like this:
$$\{x:x\text{ is a number that can be described in less that 20 English words}\}$$
This is due mainly to the lack of rigour in definition. Let us attempt to write $(1)$, $(2)$, and $(3)$ in a more symbolic form.
Let $\phi(p)$ be “$p$ is one of my predictions”
$$\tag{2}\phi(A)$$
$$\tag{3}\phi(B)$$
Now, in order to refer to $(2)$ and $(3)$ collectively, we can use the class $\{x:\phi(x)\}$. Thus, $(1)$ is defined as thus:
$$\tag{1}\text{Maj}[\{x:\phi(x)\}]$$
(The $\text{Maj}$ function is true iff at least one half of its inputs (in this case, the members of the class $\{x:\phi(x)\}$) are true.)
Using such rigour creates an output as one would expect. Now, however, what if $(1)$ was a prediction? Then $(1)$ would look something like this:
$$\tag{1}\text{Maj}[\{x:\phi(x)\}]\wedge\phi\left((1)\right)$$
Uh-oh. Self-reference!! How can we define $(1)$ whilst using $(1)$ in our definition? That's the problem. It's like defining “circular” to be “an object that is circular&rqduo;—it just doesn't work.
Happy logic-doing!
A: This doesn't seem like a contradiction to me: (1) and (3) are false, and (2) is true. 
Alternatively, we can make things more comlicated by introducing time (https://en.wikipedia.org/wiki/Temporal_logic) into the equation, so that there is a moment when (1) is true (immediately after (2) has been verified and (3) disproved)), but then (1) becomes false immediately later. But I don't see the need for this interpretation.
