roulette number repeat...two workings dif answers..1wrong-why?

Hi,

Suppose a roulette (with 38 numbers) is spun 12 times, and the probability of any number repeated is required.

So:

Working 1: 38C1*12C2*(1/38)^2*(37/38)^10.......gives a value greater than 1 so obviously wrong. (success occuring twice for a single number, then accounting for 38 separate no.s)

Working 2: No repeat= 38*37*36*..*27/(38)^12. So at least one repeat=1-no repeat=1-.143=.857 probability...looks better, and sufficient for my task.

Problem is...how do I find out the probability of any number occuring thrice exactly, or at least probability of any number occuring twice exactly, as the working 1 doesn't work, and working 2 is only applicable for the special case and no more :( Why just when I think I have learnt something about probability it eludes me. :(

Heeeelp!

Re: roulette number repeat...two workings dif answers..1wrong-why?

Quote:

Originally Posted by

**ssadi** Hi,

Suppose a roulette (with 38 numbers) is spun 12 times, and the probability of any number repeated is required.

There are $\displaystyle \mathcal{T}=\binom{12+38-1}{12}$ total of outcomes.

There are $\displaystyle \mathcal{D}=\binom{38}{12}$ ways to have **all different** outcomes.

The probability of all different outcomes is $\displaystyle \frac{\mathcal{D}}{\mathcal{T}}$.

So the probability of at least one repeated outcome is $\displaystyle 1-\frac{\mathcal{D}}{\mathcal{T}}$.

Now I am not sure that is actually what you mean by "any number repeated".

Re: roulette number repeat...two workings dif answers..1wrong-why?

no, I don't think I meant what you think I meant

You are saying the probability of a particular set of number of appearing

I am saying that say..2 appears at least twice, or 15 appears exactly 3 times... in the 12 trials

How to get that probability?

Re: roulette number repeat...two workings dif answers..1wrong-why?

Quote:

Originally Posted by

**ssadi** no, I don't think I meant what you think I meant

You are saying the probability of a particular set of number of appearing

I am saying that say..2 appears at least twice, or 15 appears exactly 3 times... in the 12 trials

How to get that probability?

In that case, you need to give a full and complete detailed description of the setup.

When you use the word *any* it does not mean a particular set.

Re: roulette number repeat...two workings dif answers..1wrong-why?

for example

12 trials

any number in the set (00,0...36) repeats itself

within the 12 trials

I don't know how i can be more specific

similarly, say

any number in the set (00, 0...36) appears exactly 3 times in the 12 trials