One of your dresser drawers contains 10 black socks and 10 blue socks. Suppose it is dark and you can’t tell what color a sock is when you look at it. If you start taking socks randomly one at a time from the drawer, how many would you have to take to guarantee that you get a pair of blue socks?
2
20
10
3
12
clearly you would have to draw 12, in case the first 10 were all black.
To guarantee that you get a pair of blue socks, you would need to take at least 3 socks. Here's how you arrive at this answer:
When you first take a sock, it could be either black or blue. Let's say you get a black sock.
Now, when you take the second sock, it could again be black or blue. If it's black, you still don't have a pair of blue socks. However, if it's blue, congratulations! You now have a pair of blue socks.
But what if the second sock is black? In that case, when you take the third sock, it has to be blue in order to guarantee that you have a pair of blue socks.
Therefore, in the worst-case scenario, where you keep getting black socks first, you would need to take at least 3 socks to guarantee that you get a pair of blue socks.
So the correct answer is 3.