5x5 board Bingo Question There is a game which I play, it is like bingo. It starts with a 5x5. 
Lets say horizontally it goes ABCDE from left to right and vertically it goes 12345 from bottom to top.
I have 2 random generators which will generate a letter and a number giving me a box to cross. So for example A2.
Suppose I the generators don't generate a box that has been generated before, what is the probability that after the Nth amount of random generations, I get a bingo horizontally or vertically. I would like to also know the probability of the Nth generation to be a bingo.

Another simple way to evaluate is probability is to use Monte Carlo Simulation,
See my python code:
from random import randint
from functools import reduce

def isBingo(board):
  for i in range(5):
    horizontal = reduce(lambda x,y: x and y, map(lambda j: board[i][j],range(5)), True)
    vertical = reduce(lambda x,y: x and y, map(lambda j: board[j][i],range(5)), True)
    if horizontal or vertical:
      return True
  return False

def monte_carlo(n, iterations=10000):
  count = 0
  for i in range(iterations):
    #Clean board
    board = [[False, False, False, False, False] for j in range(5)]
    for j in range(n):
      #Mark random square
      row = None
      column = None
      while row is None or board[row][column]:
        row = randint(0,4)
        column = randint(0,4)
      board[row][column] = True
    if isBingo(board):
      count += 1.0
  return count/iterations

For example:

print (monte_carlo(15))
0.4876

