# Thread: Probability of choosing the same number?

1. ## Probability of choosing the same number?

Hi all.

As good as I was at maths in high school, I'm afraid I never could quite grasp the Addmaths syllabus at school. Therefore, I'm not that great at probabilities

I have a slight dilemma. I'm going to try and explain this properly:

Let's assume I have two random numbers (each containing 10 digits). I now join those two 10-digit numbers to create one long 20-digit number.

Now, at random, I pick out 7 digits to create a new, smaller number. This process continues indefinitely, providing me with a long list of 7 digit numbers.

This is where my question comes in. What are the chances of picking out 7 digits that match, exactly, a previous 7 digits?

This puzzle has been worrying me for the entire morning, and like I said, I'm not that great at probabilities.

I'd really appreciate the help

Thanks,
Geoff

2. Originally Posted by garbetjie
Hi all.

As good as I was at maths in high school, I'm afraid I never could quite grasp the Addmaths syllabus at school. Therefore, I'm not that great at probabilities

I have a slight dilemma. I'm going to try and explain this properly:

Let's assume I have two random numbers (each containing 10 digits). I now join those two 10-digit numbers to create one long 20-digit number.

Now, at random, I pick out 7 digits to create a new, smaller number. This process continues indefinitely, providing me with a long list of 7 digit numbers.

This is where my question comes in. What are the chances of picking out 7 digits that match, exactly, a previous 7 digits?

This puzzle has been worrying me for the entire morning, and like I said, I'm not that great at probabilities.

I'd really appreciate the help

Thanks,
Geoff
If you do it for long enough you are certain (or at least with probability 1)
to get duplicates.

There is an ambiguity in you question, drawing 7 digits at random from
a set of 20 does not guarantee that you get a 7 digit number. The
digit drawn for the most significant position in the 7 digit number may be a
zero, which gives at most a six digit number.

I expect there are more side conditions that you need to add to this
question before you have pinned down your real question.

Note each of {0, 1, 2, ...9} in your set of 20 digits does not occur with
equal probability as the leading digits of your 10 digit numbers cannot be zero).

RonL

3. I'm assuming that when you say the most significant number, you're meaning the very first digit in the 7 digit number?

The thing is, this code would be used in a website, where an item is given a unique 7 digit code. So I would never need to worry about the first digit of the code being 0. There won't ever be more than say 1000 000 items, so I suppose when I say indefinitely, I'm not being quite truthful

4. Originally Posted by garbetjie
I'm assuming that when you say the most significant number, you're meaning the very first digit in the 7 digit number?

The thing is, this code would be used in a website, where an item is given a unique 7 digit code. So I would never need to worry about the first digit of the code being 0. There won't ever be more than say 1000 000 items, so I suppose when I say indefinitely, I'm not being quite truthful
So the leading digits can be 0?

RonL

5. Yip, they can.