What are the odds?

[littletent]

As a child I had a bike with the alphanumeric serial AD93847. A few weeks ago I registered with a web service and was issued the registration Alphanumeric AD93847 - Identical to the bike reg. What is the probability for this happening?

[jake-the-peg]

You have to be careful of what you are asking.

Do you mean:

What are the odds that you get a bike with that serial number and you then register with a particular web service and get the same - Astronomical

What are the odds that you What are the odds that you get a bike with that serial number and you then register with some other service and get the same - eg library card, membership number to a club, etc. - Coming down a bit

or

What are the odds that you get a serial number on something (not necessarilly a bike) and then get the same serial number elsewhere at a later stage - surprisingly low.



You see probabilities have a habit of playing tricks on our expectations. You only have to get a relatively few people in a room to have quite a high probaility that 2 share a birthday.

I think about thirty something gives you a 50% chance.

If you really want your mind blown about probability check out the Monty hall game here:

http://math.ucsd.edu/~crypto/Monty/monty.html

3 doors - you have to pick the one with a car behind

After you pick a different door is opened and you get the chance to change your mind and pick a different door- if you do your chances of winning are better

[chakka35]

It's 23 people, Jake, to get an evens chance.

The answer to littletent's question depends on what system is used to to arrive at the reg numbers. If, for example, they all start with AD then we can discount the letters.

If, on the other hand, all letters and digits are allowed then the chance is one in 26x26x10x10x10x10x10, which is one in 67,600,000.

The Monty Hall thing is truly amazing. When I first heard of it I didn't believe it, like most people. But in the end reason prevailed and it now seems so obvious that I wonder what my problem was.

[Teddio]

Thanks for the Monty Hall link Jake. Amazingly counter-intuitive!

[dundurn]

The odds against getting the same serial number are a bit higher than Chakka has given. The odds are correct if you assume that all serial numbers are 7 digits long with the first two letters and the rest numbers, but lots of serial numbers don't conform to this pattern. Simply assuming a 7 character serial number would result in odds of 36x36x36x36x36x36x36 = 1 in 78,364,164,096

[heathfield]

Do not questions the workings of the Universe on its own behalf. It's always busy, busy, busy!

[chakka35]

You're right, of course, dundurn, but your hypothetical system is far-fetched. Alphanumeric codes don't usually work like that. But they could.. they could...

[karatant]

If your giving a true account then the possibility is a certainty !