If you have 50 black marbles and 50 white marbles in a bag at most how many times would you have to draw out a marble to get two the same colour?

The maximum number of marbles you have to draw is three. 1) Draw a marble. It is either white or black. 2) Draw a second marble. If it is the same colour as the first marble, we are done after two draws. 3) Otherwise, the drawn marbles have different colours. Draw a third marble.

No matter what you draw next, you must have two marbles of the same colour.