Probability help!!!!!!!!!!!!!!!

If there are 20 socks in a box,10 red and 10 blue.in a dark room,how many socks one will have to take out to ensure that he takes out exactly 2 blue socks.
the given answer is 12,pls explain the proceedings in detail

Not much in detail,

the first 10 socks you pick could all be red, the next 2 guarantee you have a pair of blue socks

10 + 2 = 12

Put yourself in that position. Say you're in a dark room and Jigsaw's playing a game where you have to exit the room with at least two blue socks. The key word here is "ensure". The fact that you have to exit the room with AT LEAST two socks. You can exit with more than two socks. No problem. But at the very very minimum, you have to exit with two blue socks.
Now you're in the room. You take out a sock. It could be a red or a blue. You take out another one. Same thing. Now you have two socks. They could both be blue, or both be red, or one blue, one red. BUT YOU CAN'T BE SURE. Now let's say you take out 10 red socks. Some of those socks could be blue, sure. BUT THERE IS STILL A SMALL PROBABILITY ALL COULD BE RED. If that's the case, then the next sock you take out would HAVE to be BLUE. And so will the next sock. When you do this in practice, sure, taking out 12 socks could mean you take out more than 2 blue socks. But at the VERY LEAST, you'll have AT LEAST 2 blue socks.

It's possible that the first 10 socks taken will all be red.
After that, all the remaining socks are blue, so the next two socks taken must be blue.
Therefore, one must take a maximum of 12 socks to ensure that at least two blue socks are taken.