a bag has 6 marbles in it each marble is either red blue or green what is the least number of marbles that you must pull out of the bag to be sure you have two marbles the same color?
To determine the least number of marbles you must pull out of the bag to be sure you have two marbles of the same color, you need to consider the worst-case scenario. This means assuming that you consistently pick marbles of different colors until you can be certain that you have two marbles of the same color.
One approach to solving this problem is using the Pigeonhole Principle. The principle states that if you have n+1 objects to distribute into n containers, there must be at least one container with two or more objects.
In this case, each different color (red, blue, and green) represents a container, and the marbles represent the objects. According to the Pigeonhole Principle, you need to have one more object (marble) than the number of containers (colors) in order to be certain that you have at least two marbles of the same color.
Since you have three different colors (containers), you will need to pull out a minimum of four marbles. In the worst-case scenario, the first three marbles you pull could be different colors (one red, one blue, and one green), but the fourth marble you pull will have to match one of the previous colors, ensuring that you have two marbles of the same color.
Therefore, the least number of marbles you must pull out of the bag to be sure you have two marbles of the same color is four.