Hypothetical "Ball Pool"

ikoonman

Hi

I have a question for all you math whizz kids out there. Unfortunately my maths isn't the best so I hope you can help me.

Say I have a hypothetical ball pool, with a number of different simple shape objects, how can I statistically determine the most likely color AND shape to occur? (If you are really a sucker for punishment you can even throw in size... )

Thanks in advance

Yakuza

Not quite sure what you mean, but here goes...

If there are, say, 4 colours (red, yellow, green, blue) and 3 shapes (cube, sphere and pyramid) then (again, assuming a large number of objects in the bag, and that they are evenly distributed)

1) P(object you choose is red) = 1/4
2) p(object you choose is a sphere) = 1/3
3) p(object you choose is a red sphere) = 1/4 * 1/3 = 1/12.

The only way to determine the *most* likely shape and colour is if you know the relative proportions of all shapes and colours.

If you could clarify your question a little more, that would be of great help

ikoonman

Hi

Thanks for your reply. Sorry if my description is a bit vague. You can assume that you know how many objects there are, and the types of colors and shapes it can be.

Given this, you can prob put this in some sort of matrix and then perform your calculation based on that.

Does this help? If it's still not sufficient info, ask away and I'll fill the blanks.

TIA

Yakuza

I think you've answered your own question

A matrix would be perfect for this...put the colour on the top and the shape down the sides, and categorise all the shapes into their colours:

________|R |G |Y |B
Cube____|2 |3 |1 |1
Sphere__|1 |5 |2 |2
Pyramid_ |4 |1 |4 |4

Then, you determine the probabilities of the various objects by dividing the number in the appropriate cell by the total number of objects in the matrix (30)

smiles

Bayes Theorem all the way....

I assume you'll be asking a question along the lines of "I have a blue object, what is the probability it is a cube?"



Simple example: you have 2 colors: red and blue, and 2 items, cubes and spheres.

Here B is event of a blue item, A is the event of a cube.

P(A|B) is the probability the item is a cube, given it is blue.
P(B|A) is the probability the item is blue given that it is a cube. (should be given)
P(A) is the probability any item you select is a cube (also should be given) (ie. number of cubes / total number of items)
P(B) is the probability any item you select is blue (should be given) (ie. number of blue items / total number of items)

Hope that helps