You have a bag that contains fifty pebbles, twenty-five painted white and twenty-five painted black.

You randomly remove two pebbles.

If either of them is white, discard it and put the other pebble (whether it is black or white) back into the bag.

If both are black, discard both of them.

You repeat this process until there is only one pebble in the bag, what is the probability that the final pebble is white?