in a bag there are 3 different marble colors. what is the minimum marble does one have to remove in order to get 3 marble of the same color? * i know this is a probability question but since it does not give you the individual amount i don't think i can get an answer
The minimum (least) is 3, the maximum (most) is something different. If the first three are different, the fourth will be a duplicate of one of these. If the next two duplicate the other colors, the following marble will give you 3 of the same color.
59 marbles
To determine the minimum number of marbles one must remove from the bag in order to get 3 marbles of the same color, we can analyze the worst-case scenario for each possible situation.
Let's consider the three marble colors as A, B, and C.
In the worst-case scenario, we want to remove marbles of two different colors until we force the occurrence of the third color.
Assuming the bag initially contains one marble of each color (A, B, and C), the worst-case sequence of removals would be as follows:
1. Remove marble A.
2. Remove marble B.
3. Remove marble A.
At this point, regardless of the color of the fourth marble removed, we are guaranteed to have three marbles of the same color among the four removed. Therefore, the minimum number of marbles needed to be removed is 3.
It is important to note that this explanation assumes that the bag contains an unlimited number of marbles of each color. If there is a limited number of marbles for each color, the probability calculation would be necessary to obtain an exact answer.