1. ## Spinning Wheels

I have two wheels which have been spun 20 times and the numbers were recorded. However i now no longer have the numbers that used to be on the wheel! I do however know the highest and lowest possible outcomes were spun but i now need to, using probability, find out the numbers that used to be on the wheels and how much space on the wheels they take up.

0,0,0,0,0,0,0,0,1,1,2,10,10,11,11,11,12,12,12,13

As this is an assignment i would appreciated it if you didn't answer the question, but just gave me a nudge in the right direction or give me some sort of strategy to answering questions like these.

2. Two wheels? Are there different numbers on different wheels?

With two different wheels, and no information as to what numbers are on which wheel and which outcome came from which wheel, I don't believe it can be done.

If it were true that the two wheels are identical, then we could treat it as a single wheel. And are we too assume that every integer between lowest and highest is on the wheel?

Since you say lowest and highest did come up, it is easy to see that the lowest number on the wheel is 0 and the highest is 13- those are the lowest and highest numbers that came up. Assuming all numbers between those are on the wheel, we must have 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. Now presumably the probability a number comes up is proportional to the space it takes up. For example, 0 came up 8 times, 2 only once so the area 0 takes up must be 8 times as large as the area 2 takes up. But what are we going to do with numbers that didn't come up? The area for them must be relatively small but how small should we make it?