To determine how many gloves the woman must remove to be certain she has a matching pair for herself and her daughter, we need to consider the worst-case scenario.
In this case, the worst-case scenario would be if she selects gloves of different colors each time. Therefore, she would need to remove gloves until she has at least one of each color. After that, the next glove she removes would guarantee a matching pair.
Let's go through each option to see which one is correct:
Option A) 7 - This option is incorrect because it assumes that the woman can have a matching pair after removing 7 gloves. However, it is possible that she could have selected gloves of all three colors (black, white, and red) without getting a matching pair.
Option B) 6 - This option is correct. If the woman removes 6 gloves, it is guaranteed that she will have at least one of each color. The next glove she removes would guarantee a matching pair.
Option C) 9 - This option is incorrect because it assumes that the woman needs to remove 9 gloves to have a matching pair. However, she could have selected gloves of all three colors (black, white, and red) before reaching 9 gloves.
Option D) 8 - This option is incorrect for the same reason as option C. It assumes that the woman needs to remove 8 gloves to have a matching pair, but she could have selected gloves of all three colors before reaching 8 gloves.
Therefore, the correct answer is B) 6.