Mr. Brown has 6 black gloves and 8 brown gloves in his closet. He blindly picks up some gloves from the closet. What is the minimum number of gloves Mr. Brown will have to pick to be certain to find a pair of gloves of the same color?

  1. 2

  2. 3

  3. 7

  4. 9


Correct Option: B

AI Explanation

To answer this question, we need to consider the worst-case scenario where Mr. Brown picks gloves in such a way that he does not find a matching pair.

In this case, the worst-case scenario would be if he picks all the black gloves first and then starts picking the brown gloves. In this scenario, he would need to pick at least 7 gloves (all 6 black gloves and 1 brown glove) to be certain to find a pair of gloves of the same color.

Therefore, the minimum number of gloves Mr. Brown will have to pick to be certain to find a pair of gloves of the same color is 7.

Let's go through each option to understand why it is correct or incorrect:

Option A) 2 - This option is incorrect because Mr. Brown may pick one black glove and one brown glove, which would not give him a pair of gloves of the same color. Option B) 3 - This option is correct because Mr. Brown may pick two black gloves and one brown glove, which would give him a pair of black gloves. Option C) 7 - This option is incorrect because Mr. Brown would need to pick all 6 black gloves and 1 brown glove to be certain to find a pair of gloves of the same color. Option D) 9 - This option is incorrect because Mr. Brown would need to pick all 6 black gloves and all 8 brown gloves to be certain to find a pair of gloves of the same color.

The correct answer is B) 3. This option is correct because Mr. Brown may pick two black gloves and one brown glove, which would give him a pair of black gloves.

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