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1. A bag contains 3 red, 4 white and 5 blue marbles. Jason begins removing marbles from the bag at random, one at a time. what is the least number of marbles he must remove to sure that he has at least one of each color?
- A. 3
- B. 3
- C. 3
- D. 3
Answer: Option D
Explanation:
To be sure that Jason has at least one marble of each color (red, white, and blue), he should continue removing marbles until he has exhausted all of one color. In this case, we want to find the least number of marbles he must remove to ensure he has at least one marble of each color.
The maximum number of marbles of a single color (blue, in this case) is 5. So, Jason must remove all the white and red marbles first before he can be sure he has at least one marble of each color.
Number of white and red marbles = 4 white + 3 red = 7
Now, Jason must remove all 7 of these marbles before he can be sure he has at least one marble of each color.
Therefore, the least number of marbles he must remove is 7 (to remove all the white and red marbles) + 3 (to remove the remaining red marbles) = 10.
So, the least number of marbles he must remove to ensure he has at least one of each color is 10.
The correct answer is 10.
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