1. Increasing Chances - ratio

The ratio of red marbles to green marbles in a container is 3 to 5. How many red marbles should you add to the container with "n" green marbles so that the probability of getting a red marble is 7/8? Give your answer in terms of "n".

2. Re: Increasing Chances - ratio

How many red marbles are in the container initially?

3. Re: Increasing Chances - ratio

It doesn't say. That's the question word for word. Here is the link where it orginiated from:

InterMath

I don't know where to start to answer it.

4. Re: Increasing Chances - ratio

I agree that the question does not say how many red marbles are there. You can start to answer it by figuring out the initial number of red marbles in terms of n. If you can't do this, my guess would be that you don't fully understand all the information given in the problem. In this case, you should ask what this information means.

5. Re: Increasing Chances - ratio

I began thinking about this .. If the ratio of red to green is 3 to 5 .. there would be 3 red marbles and 5 green marbles. So I understand that portion of the question. Is there a formula I should use to figure out the second part of the question? Or is this a trial and error type thing?

6. Re: Increasing Chances - ratio

Originally Posted by jthomp18
If the ratio of red to green is 3 to 5 .. there would be 3 red marbles and 5 green marbles.
No, there would be 3 red marbles to each group of 5 green marbles. There are n green marbles, so there are n / 5 groups of 5, so there are 3n / 5 red marbles initially. Now you add some unknown number x of red marbles, and the ratio of red to green becomes 7 / 8. Form an equation in x and solve it (i.e., express x through n).

7. Re: Increasing Chances - ratio

I am trying to figure out the equation. I sort of understand your statement above. But, I am still lost as how to set up the equation. I'm sorry, I really am trying to comrprehend this material. This is part of a project our professor has us doing. & the class is only offered online. He would never help me out as much as you have. I am just not that great with math. I really am trying to understand this question. Is there any way to describe it deeper to where I can learn how to set up the formula?

8. Re: Increasing Chances - ratio

The ratio of any two numbers u and v is u / v. You know the initial number of red marbles and how many were added (i.e., x). The problem also gives the number of green marbles. Find the ratio of red to green after the addition and equate it to 7 / 8.

9. Re: Increasing Chances - ratio

Originally Posted by jthomp18
The ratio of red marbles to green marbles in a container is 3 to 5. How many red marbles should you add to the container with "n" green marbles so that the probability of getting a red marble is 7/8? Give your answer in terms of "n".
How about adding: $40 k [-(3/5) + 7 n/8], k=1,2,3,....$