You have a bag of lots of red and white marbles. In the worst case, how many would you have to pull out to get two marbles of the same color? Four? Generalize by finding a formula for predicting the maximum number of marbles that you would have to pull out to get the same color of any amount you desire.
What if there were three colors of marbles in the bag, how many would you have to pull out to get two marbles of the same color? Three? Four? Generalize by finding a formula for predicting the number of marbles you would have to pull out to get the same color of any amount you desire.
but its in the WORST case scenario
You didn't really answer the question at all
To determine the maximum number of marbles you would have to pull out to get two marbles of the same color, we can use the worst-case scenario where you alternate colors as you pull marbles out.
If there are two colors of marbles in the bag (let's say red and white), you would have to pull out 4 marbles to guarantee getting two marbles of the same color. Here's how it would play out:
1. The first marble can be any color.
2. The second marble can be of a different color than the first.
3. The third marble must be different from both the first and second.
4. The fourth marble will either match one of the previous three, guaranteeing two marbles of the same color.
Thus, in the worst case, you would need to pull out at least four marbles.
To generalize this scenario, we can use the formula:
n + 1
where "n" is the number of colors of marbles in the bag.
For example, if there are three colors of marbles in the bag, the formula would be:
3 + 1 = 4
Therefore, you would have to pull out a minimum of four marbles to guarantee getting two marbles of the same color.
Feel free to ask if anything is unclear or if you have any further questions!
To determine the maximum number of marbles you would have to pull out to get two marbles of the same color, you need to consider the worst-case scenario.
For the case of two colors (red and white) in the bag, in the worst case, you would have to pull out four marbles. This is because you might first pull out a red marble, followed by a white marble, then another red marble, and finally a white marble, giving you two marbles of the same color.
To generalize this for any number of marbles, you can use the formula n + 1, where n is the number of desired marbles of the same color. In the example above, n=2, so the formula would be 2 + 1 = 3.
Now, let's consider the case of three colors (red, white, and blue) in the bag. To find the maximum number of marbles needed to get two marbles of the same color, we need to consider the worst-case scenario again.
In the worst case, you would have to pull out six marbles. This could happen, for example, if you first pull out a red marble, followed by a white marble, then a blue marble, another red marble, a white marble, and finally a blue marble, giving you two red marbles.
To generalize this for any number of marbles, you can still use the formula n + 1, where n is the number of desired marbles of the same color. In this example, n=2, so the formula would be 2 + 1 = 3, just like in the previous case.
In conclusion, the maximum number of marbles you would have to pull out to get two marbles of the same color can be predicted by using the formula n + 1, where n is the number of desired marbles of the same color. This formula works for any number of colors present in the bag.
Asume you get one of each color in the first draws. Then the next draw would certainly repeat one of the colors.
That should start you out in getting your formula. Let c = number of colors and n = number of marbles you want of the same color.