Conditionally selecting random element from array

Confusing explanation

According to your explanation, storing 10 in the board means displaying \$2^{10}\$ or 1024 on the screen. If so, then storing a 1 in the board would display \$2^1\$ or 2, and storing a 2 would display \$2^2\$ or 4. But this contradicts your program which chooses a new display value of 1 and 2 using board values 1 and 2.

Either you should be generating board values 0 and 1, or your explanation was wrong. I'm guessing that your explanation was wrong and that storing x in your board represents \$2^{x-1}\$ and not \$2^x\$.

Random number generation off by one

You said you wanted to generate 1 with 90% frequency, but you actually are generating it with 89% frequency. You need to change your < to a <= to fix that.

One easy way to see that you are off by one is if you change the 90 to a 100. Then you will see that you still have a 1% chance of generating a 2 instead of a 0% chance.

Deterministic way of choosing empty cell

Instead of randomly picking cells until you get an empty one, you can count the number of empty cells, then pick among them. For example, if you count 5 empty cells, then you can pick a number between 0 and 4, and then go back through the cells and find the nth empty cell, where n is the random number you picked.

Sample rewrite

Here is an example of how you could implement the above suggestion:

void randCell(int _board[BOARD_SIZE][BOARD_SIZE]) {
    int num_spaces = 0;

    // Count the number of empty spaces.
    for (int i = 0; i < BOARD_SIZE; ++i) {
        for (int j = 0; j < BOARD_SIZE; ++j) {
            if (_board[i][j] == EMPTY)
                num_spaces++;
        }
    }

    if (num_spaces == 0)
        return;

    int rand_space = randRange(0, num_spaces - 1);
    for (int i = 0; i < BOARD_SIZE; ++i) {
        for (int j = 0; j < BOARD_SIZE; ++j) {
            if (rand_space-- == 0) {
                _board[i][i] = (randRange(1, 100) <= 90) ? 1 : 2;
                return;
            }
        }
    }
}