The box contains 100 black and 100 white balls. What is the smallest number of balls you need to pull out without

The box contains 100 black and 100 white balls. What is the smallest number of balls you need to pull out without looking into the box, so that among them there are probably a) 2 balls of the same color b) 2 white balls.

1) With the best outcome, 2 balls of the same color can be pulled out of the box 2 times in a row. If the balls are of different colors, then in the next 3 step you can pull out a ball of one of the 2 available colors, i.e. in 3 steps we will surely pull out balls of the same colors.
2) You can also consider the option in which 2 white balls will immediately fall in a row. If all the time only black balls will come across, then only 101 times will we get the white ball for sure, and in 102 steps – the second white ball.