A drawer contains 4 red socks and 4 blue socks. Find the least number of socks that must be drawn from the drawer to be assured of having a pair of red socks
Well, I guess you could start by looking for a drawer that only contains red socks. That seems to be the most assured way of getting a pair of red socks. But if we're stuck with this drawer, let's see how many socks we need to pull out.
First, we'll grab one sock. It could be either red or blue. Then, we'll take out another sock. There are three possibilities now:
1. It's the same color as the first sock, so we have a pair of red socks. Success!
2. It's the opposite color, so now we have one red sock and one blue sock.
3. It's the same color as the second sock, but different from the first sock. So, now we have two blue socks and one red sock.
In the worst-case scenario, we end up with two blue socks and one red sock after drawing three socks. But fear not! The fourth sock will surely complete our pair of red socks. So, to be absolutely assured of having a pair of red socks, you need to draw a minimum of four socks.
But remember, life is full of surprises, so you never know when you might accidentally grab a polka-dotted pair or a sock that sings show tunes!
To be assured of having a pair of red socks, we need to consider the worst-case scenario. This means that every sock drawn from the drawer is a blue sock until the very last sock.
To find the least number of socks we must draw to be assured of having a pair of red socks, we have to determine the maximum number of blue socks that can be drawn before we draw a red sock.
If we draw all 4 blue socks first, we will then have drawn 4 socks. However, if we draw one more sock, it will be a red sock, and we will have a pair of red socks.
Therefore, the least number of socks that must be drawn from the drawer to be assured of having a pair of red socks is 5.
To be assured of having a pair of red socks, the worst-case scenario would be if you drew all the blue socks before drawing any red socks. In that case, you would need to draw all the blue socks plus one red sock to have a pair of red socks.
Since there are 4 blue socks and 4 red socks, you would need to draw all 4 blue socks, which guarantees that you have no more blue socks left in the drawer. Then, when you draw the next sock, it will be a red sock, giving you the pair of red socks you were looking for.
Therefore, the least number of socks you need to draw from the drawer to be assured of having a pair of red socks is 4 blue socks + 1 red sock = 5 socks.