Maths gurus, what is the probability of this?

[alfa daley]

I am looking into running a free competition at an exhibition but can't quite get my head around the probability of someone winning.

It's going to be a crack the safe competition with prizes for, you guessed it, cracking the safe. I have a 4 digit lock on the safe which will gIve players a 1 in 10,000 chance of winning but that sounds really low to me, so what would the odds be if I told players there was a 0 in the combination but not whether it was the first, second, third or forth digit. my brain is hurting and all memories of A level stats class have faded away...

can anyone help?

[CaptainSlow]

my guess is 1 in 2,250

ETA can there be more than one 0?

Edited by CaptainSlow on Monday 1st June 21:06

[sstein]

alfa daley said:

I am looking into running a free competition at an exhibition but can't quite get my head around the probability of someone winning.

It's going to be a crack the safe competition with prizes for, you guessed it, cracking the safe. I have a 4 digit lock on the safe which will gIve players a 1 in 10,000 chance of winning but that sounds really low to me, so what would the odds be if I told players there was a 0 in the combination but not whether it was the first, second, third or forth digit. my brain is hurting and all memories of A level stats class have faded away...

can anyone help?

Do you want all the combinations from 0000 - 9999, in that case it's your 1 in 10,000.

Or do you want 1111 - 9999 but with no more than 1 zero in any combination ?

i.e. you could have 1012 but not 1010 ?

[Ayahuasca]

There would be a 1 in four chance of getting the 0 in the right place, so 1: 4 times 1000 (10 x 10 x 10 for the remaining wheels) so one in 4,000 instead of 1 in ten thousand.

Would be my guess.

[_dodge_]

Might be a little rusty, but from memory....

4 digit lock gives probability of

10c1 x 10c1 x 10c1 x 10c1 = 1 in 10,000 as you mention so if you tell them there is a zero it becomes

4c1 x 10c1 x 10c1 x 10c1 = 1 in 4000

[_dodge_]

_dodge_ said:

Might be a little rusty, but from memory....

4 digit lock gives probability of

10c1 x 10c1 x 10c1 x 10c1 = 1 in 10,000 as you mention so if you tell them there is a zero it becomes

4c1 x 10c1 x 10c1 x 10c1 = 1 in 4000

Doh, too late!

[CaptainSlow]

not sure how you're doing your maths, is it not (assuming more than one 0 allowed):

9*10*10*10+10*9*10*10+10*10*9*10+10*10*10*9 = 4 in 9,000 or 1 in 2,250

[Murray993]

try something easier. if you dont get it neither will they and it will seem like a rip off

[_dodge_]

CaptainSlow said:

not sure how you're doing your maths, is it not (assuming more than one 0 allowed):

9*10*10*10 + 10*9*10*10 + 10*10*9*10 + 10*10*10*9 = 4 in 9,000 or 1 in 2,250

My logic was, if you were to say there is at least one zero in the combination.

Then people first have a 1 in 4 chance of putting that zero in the right place, they then have 3 lots of 1 in 10 to get the remaining 3 digits.

So 4 x 10 x 10 x 10.

If he was to say there is 1 zero in the combination then I think the probability would be..

4c1 x 9c1 x 9c1 x 9c1 = 1 in 2916. (4 x 9 x 9 x 9).

Edited by _dodge_ on Monday 1st June 21:38

[johnnywgk]

with out elimenating other numbers tried by previous triers, people could be trying for 10 years and not get the right combi,

then the next hour, 20 people might get it correct.

[Neil_H]

Just get a 3 digit lock.

[M400 NBL]

I'd probably waste my money on the lottery. I'd have no chace winning that either.

How about a guess the amount of something in the safe (1p's for instance or whatever can fill it to its capacity) with the closest guess winning the prize.

[Odie]

Neil_H said:

Just get a 3 digit lock.

Or make up a riddle that gives one of the numbers and its position. So its both guess work and skill.

[WorAl]

AAAAAARRRRRRGGGHHHHHHHH MY BRAIN IS MELLLTTIIING.........

[Ayahuasca]

Odie said:

Neil_H said:

Just get a 3 digit lock.

Or make up a riddle that gives one of the numbers and its position. So its both guess work and skill.

My first is in 101 but not in 200.

My second is in 43 but not in 12

My forth is in the square root of 81 times 2 but not in the cube root of 9

My fifth, well, could be anything.

Etc...

Like that you mean?

[Justayellowbadge]

Odie said:

Neil_H said:

Just get a 3 digit lock.

Or make up a riddle that gives one of the numbers and its position. So its both guess work and skill.

But then one of your kind would turn up and just 'know' the combination.

[Neil_H]

Have you considered a raffle?

[Ayahuasca]

Neil_H said:

Have you considered a raffle?

What, in cayse inny bliks win?

[911motorsport]

Where is this exhibition of which you speak? only I might book a day off work to have a go at your 'enter the safe code' game; such is the excitement it promises it's eager contestants

Edited by 911motorsport on Tuesday 2nd June 13:50

[Neil_H]

Ayahuasca said:

Neil_H said:

Have you considered a raffle?

What, in cayse inny bliks win?

Not thit koinda raffle mate, besoids, we jast burn thim with gasoline nardays, it's cheaper thin raffle ammo.