In his pocket, a boy has 3 red marbles, 4 blue marbles, and 4 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?
To ensure that the boy has taken out at least one marble of each color (red, blue, and green), we should find the worst-case scenario, where he initially takes out the maximum number of marbles of one color before drawing a marble of a different color.
In this case, he has 4 blue marbles, so he can take out all 4 blue marbles before getting to the other colors. After taking out the 4 blue marbles, he will have taken out all of one color, but he still needs to get at least one of each of the other two colors (red and green).
So, he will need to take out 1 red marble and 1 green marble to ensure that he has at least one of each color.
Therefore, he needs to take out a total of:
4 blue marbles + 1 red marble + 1 green marble = 6 marbles
However, the question asks how many marbles he will have to take out in total, so we need to add the 3 marbles he initially took out (3 red marbles). Therefore, the total number of marbles he needs to take out to ensure he has taken out at least one of each color is:
6 marbles (for red, blue, and green) + 3 marbles (initial red marbles) = 9 marbles
So, he will have to take out a total of 9 marbles. The correct answer is 9.
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