Final answer:
Ken must draw 5 socks to guarantee he has a pair. He must account for the worst-case scenario where he draws one of each color and then one more to ensure a pair.
Step-by-step explanation:
To ensure he gets a pair of the same color, Ken must account for the worst-case scenario where he draws all different colors before getting a matching pair. Ken must pull out all four colors, which is: one black, one white, one argyle, and one green.
However, as he has only 2 argyle socks, after picking one of each of the other colors, the next sock will either be a black, a white, or a green sock, giving him a guaranteed pair of the same color.
Therefore, Ken must pull out 1 black + 1 white + 2 argyle + 1 more sock = 5 socks to guarantee he has at least one pair.
The answer to this question is d) 5 socks.