In a dark room there is a box with 8 red and 5 black socks 

1. what is the minimum number of socks you need to take to guarantee a pair of the same color ?
2. what is the minimum number of socks you need to take to guarantee a pair of red socks ?
3. and if you need to make a pair of red and a pair of black socks ?
4. 7 socks are removed from the box described in the previous problem what is probability that this sample will have exactly one pair of black socks ?