Imagine that you have 5 blue socks and 5 brown socks in a drawer that are not paired up. How many socks must you take out from the drawer (without looking) to be sure of getting a pair of the same color? (3 points)
To figure out how many socks you must take out from the drawer to be sure of getting a pair of the same color, let's analyze the worst-case scenario. In this scenario, you want to minimize the number of socks you take out while ensuring that you have a pair of the same color.
The worst-case scenario occurs when you take out one color sock at a time until you have one of each color. In this case, you would first take out one blue sock, then one brown sock, then another blue sock, and finally another brown sock. You would have taken out a total of 4 socks without having a pair of the same color.
Now, to ensure that you have a pair of the same color, the next sock you take out from the drawer will complete a pair. So, at most, you would need to take out one more sock. Therefore, in the worst-case scenario, you would need to take out a total of 4 + 1 = 5 socks to be sure of getting a pair of the same color.
Hence, you would need to take out a minimum of 5 socks from the drawer to guarantee having a pair of the same color.