Math/probability question

[saturnotaku]

I was driving to get my lunch this afternoon and thought of something that I need the help of a math guru to determine.

Let me preface this by saying that the government of the state of Illinois, especially the Secretary of State's office is run by retarded monkeys. The newest random number scheme of Illinois license plates is composed of 7 characters, entirely numbers (ie 123 4567). It's a completely assinine scheme, and all the other possibilities for random numbers have pretty much been used.

That said, I was wondering how one would go about determining the odds of receiving a plate that is made up entirely of odd numbers or entirely of even numbers. My plate is made up of the latter.

Since I haven't taken a math class in over 5 years, I'm really rusty on this sort of thing so if any of you math wizards can help me out, that'd be cool. :cool:

[de><ta]

0.5 ^ 7 = 0.0078125

works out to o.78125 %
out of a possible 1000 0000 different possible number plates.

number of folks with number plates consisting of all odd or all evens : 781 2500

hmm i wonder why i posted this... :confused:
i guess i had an urge to solve something.... wierd.:confused:

[saturnotaku]

Don't you mean 78,125 out of a possible 10,000,000? Or am I missing something? :confused:

In any case, thanks for the fast reply. :mohawk:

[de><ta]

oops
it is 78, 125

forgot that 0.0078125 it self was over 100.

if it were 781250 your number plate wouldnt be that special.:D

[saturnotaku]

I was just thinking of something. Zero can't be the first number so that will make the number of combinations somewhat less. Now exactly how many...I have no idea so that's where you come in. :D

[de><ta]

oh great now people are going to start calling me a nerd around here...:D

if the first no. cant be a 0,
then for odd possibilities it remains the same, since 0 is not odd,

hmmm just occured to me, there is bit more stat to this problem, technically you cant have an all 00000 num plate and you cant have one starting with 0's

therefore number of number plates with even only numbers, with this new fact.

0.4*(0.5^6) = dont have my ti 89 so shug

i am not sure, i think in this case you have to use nCr or nPr, its been a quarter since i took discrete, boy i am going to be a top notch employee...:D

[Shinri Hikari]

Good to see that someone cares... nice shot de><ta.;) Somewhat odd that the licence plate has numbers only, but not unprecidented. That will change due to the limited possibilities in a numbers only scheam.

[legion88]

Originally posted by saturnotaku
I was driving to get my lunch this afternoon and thought of something that I need the help of a math guru to determine.

Let me preface this by saying that the government of the state of Illinois, especially the Secretary of State's office is run by retarded monkeys. The newest random number scheme of Illinois license plates is composed of 7 characters, entirely numbers (ie 123 4567). It's a completely assinine scheme, and all the other possibilities for random numbers have pretty much been used.

That said, I was wondering how one would go about determining the odds of receiving a plate that is made up entirely of odd numbers or entirely of even numbers. My plate is made up of the latter.

Since I haven't taken a math class in over 5 years, I'm really rusty on this sort of thing so if any of you math wizards can help me out, that'd be cool. :cool:

So, you are telling me that your state is planning to have only 9 million license plates? Remember, the first digit can't be zero. So all #s from 0,000,000 to 0,999,999 are forbidden.

[saturnotaku]

Originally posted by legion88
So, you are telling me that your state is planning to have only 9 million license plates?

No, I probably should have added to my preface that it appears the state has exhausted every other possible random number scheme.

ABC 123, AB 1234 have all been used
A 123 456 - all gone
ABC 1234 - reserved for vanity/personalized
ABC 12 - same as above

Putting the numbers first is a system reserved for pickups and other classes of trucks (except SUV's).

Once we hit the plate 999 9999, I have to wonder what the state is going to do after that. :confused:

Right now, the highest plate number I've seen has the first three numbers as 510 so we're more than halfway to exhausing the scheme, which was started in Aug. 2001.

Anyway, I knew I'd be throwing a monkey wrench into the equation when I said you couldn't have a 0 be the first number. Thanks de><ta for helping out with this. Perhaps you could do a paper/project on this question hehehe. :D

[Shinri Hikari]

Maybe they will start using picture combos:D. Or they could recycle the old numbers. Perhaps both...:p :cool: Or maybe barcodes.:rolleyes: :eek:

[krakatoa]

Well if you thought that your system was complex, try and get your head around the UK system.

Began with the style - ABC 123 A (Excluding the letters IOQZ and the number 0, Q is used for kit or self assemble cars).
Then this scheme was used up so went for - A 123 ABC (Same exclusions as above)

This was changed to the latest system 2 years ago which is.

Any car bought between April and August will have the plate :

AA 03 ABC where the first two letters represent the county the car was purchased from and the numbers represent the year the car was purchased, ie LS=London, 03=2003 ABC=random combination of any three letters.

And those cars bought between September and March have the plate :

AA 53 ABC where the first two letters represent the county the car was purchased from and the numbers represent the year the car was purchased, ie LS=London, 53=2003 ABC=random combination of any three letters.

Plus there is also a range of personalised plates that can contain any combination of the valid range of data.

So could this system qualify as the most complicated licensing system for cars in the world????