# Distribution of balls in a box (with a twist)

1. May 15, 2014

### Apteronotus

Suppose I have an box (set) containing two different colored balls, red and blue, say.

Now, suppose the balls differ in size, where the size of the red balls has one particular distribution and those of the blue another.

How can we describe the distribution of the balls in the box?

2. May 15, 2014

### mathman

Your description is confusing. What has size got to do with the distribution?

3. May 15, 2014

### FactChecker

It's a weighted average of the PDF_red and PDF_blue, with weights proportional to the fraction of each color:

PFD_total = (num_red/total_num) * PDF_red + (num_blue/total_num) * PDF_blue

4. May 16, 2014

### Apteronotus

I'm interested in the distribution of the sizes.

5. May 16, 2014

### Apteronotus

So would it be a "mixed distribution"?

6. May 16, 2014

### FactChecker

It is a single distribution where a ball can be picked at random by a blind person and it would give the probability distribution of the size, without knowing the color. It combines the two distributions into one.

7. May 17, 2014

### FactChecker

Yes. That is called a "mixture distribution".