Question

what is the minimum amount of times you would need to reach into a box of socks that is 50 percent back socks and 50 percent white socks to be sure you pull out a matching pair?

Answer 1

To be sure you pull out a matching pair of socks from a box that contains 50% black socks and 50% white socks, you would need to reach into the box at least three times.

Let's consider the worst-case scenario. In the first two draws, you could randomly pick one black sock and one white sock, as there is an equal probability of selecting either color. However, in the third draw, you are guaranteed to have a matching pair, either two black socks or two white socks, ensuring a match.

So, at least three draws from the box would be required to be sure you pull out a matching pair of socks.