How to generate random pattern of data with specific probability?

I don't know how to change my code to generate a random pattern of alive cells. numpy is not allowed. (CellType(True) = "O"

def seed_random(self, confluency, CellType=Cell):
    self.confluency = float(confluency)
    
    x = random.uniform(0,1)
    print(x)
    cu_prob = 0.0
    test_matrix = list()
    for i in range(self.rows):
        test_matrix.append([])
        for j in range(self.cols):
            test_matrix[i].append(CellType(False))
            cu_prob += confluency
            if x < confluency:
        
                test_matrix[i][j]=CellType(True)
            else:
                test_matrix[i][j]=CellType(False)

    self.matrix = test_matrix

I want my output look like this when confluency is 0.5.

O..OOO..OO.O.OO.O..OO..OOOOOOOOOOOOO...O

..OO...O..O.....OO.OO...OO...OOOO...OO..

...O...OO..O.......OO..O.OOO...OOOO.....

O..OOO.OO.OOO.OO.OOOOOOOO..O..OOO.O...O.

..O.O.O.OO..O.O..OOO.O...O....OOO.OOO.OO

O..OOO..OO...O..O.O.OO.O...OOO....O.OOO.

..O..O.OOO...OO..O.OO.OO.OOOO.O.O..OOOO.

OO.O.OOO...OO.....O.OOOO.O...OOOO..OO...

OOOO.OO.O.O.O..O.O...OO..O.O.OO......OOO

..OO.....OOOOO.O.OOOOO.OO.OO...O..OOOOO.

but my output is either this or circles

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