Answer to Question #176301 in Statistics and Probability for Adrii

Question

If I have 10 black socks and 10 blue socks in the drawer, what is the minimum number of socks that I have to take out to have a blue pair of socks?

Answer 1

Solution:

We will have a matching pair of socks after three tries because only two socks, of either color, are needed. Assume the first sock drawn is black. There are only two things that can now happen: If the next sock is black, there's now a matching pair of socks and we're done. If the next sock is blue, there's now a blue and a black sock. Now, no matter what the next sock drawn will make a pair. Whether a black sock or a blue sock is drawn, there'll be two socks of one color and one of the other color. Therefore, there'll always be a pair by the third sock drawn.

Thus, the minimum number of socks to be taken out to have a blue pair of socks is 3.