Final answer:
The minimum number of socks needed to be sure of having 4 pairs is 12. This accounts for the worst-case scenario of picking the maximum number of non-pairing socks from each of the three colors before securing the four matching pairs.
Step-by-step explanation:
The student is asking about a probability problem in Mathematics involving socks in a drawer. The subject of the question is how to determine the least number of socks that must be taken out of a drawer to be sure of having 4 pairs of matching socks. In the worst-case scenario, you could draw out all the socks of the first two colors without getting a single pair of the third color. Once you start drawing the third color, you will get pairs. If there are three colors, and you want four pairs, you need to account for drawing the maximum number of socks without getting four pairs of one color. So you could draw:
- 3 red socks (not enough for 4 pairs),
- Plus 3 black socks (still not enough for 4 pairs),
- Plus 3 white socks (still not enough for 4 pairs).
At this point, you have 3 of each color but no 4 pairs. The next sock you draw, no matter the color, will complete a pair. Since you need four pairs, you will draw 3 more socks of that color.
So the calculation would be 3(red) + 3(black) + 3(white) + 3(same color for four pairs) = 12 socks to ensure 4 pairs.