question re probability of consecutive numbers

[ajp]

Hi all,
This is a fairly basic stastics question but it's bothering me so...
In a 4 ball lottery with possible numbers 1-10 for each ball - is it true that you will see less quad results (i.e. 4444 or 7777) than other possible number combinations?
I know the probability of a particular digit coming up in this case for each digit is 1 in 10, but isn't the probability of getting a quad lower because of the lower numbe of possible combinations - 10 possible quads versus whatever the number of other possible combinations is (is it 9990?)
I'm terrible at stats - any insight you could give would be great
thanks!
alex

 

[GillesD]

Quad or not?

Ajp

Let’s take two numbers (say 4444 and 3951) and see what the probability is in each case.

For 4444, you have 1 chance in 10 to have 4 as the first number, then 1 chance in 10 to have 4 as the second number, then 1 chance in 10 to have 4 as the third number and finally 1 chance in 10 to have 4 as the fourth number.

For 3951, you have 1 chance in 10 to have 3 as the first number, then 1 chance in 10 to have 9 as the second number, then 1 chance in 10 to have 5 as the third number and finally 1 chance in 10 to have 1 as the fourth number.

To get the overall probability, you multiply each individual probability, so it is the same for both 4444 and 3951. This amounts to 1/10 by 1/10 by 1/10 by 1/10 or 1 chance in 10,000.

 

[ajp]

Thanks...

that's what I figured. something still bugs me though:
I agree that the mathmatical probability of getting any particular number combination is the same (10^4) or 1 in 10000. However,
What I was referring to is that there are only 10 possible combinations of quad numbers whereas there are 9990 possible combinations of non quad repetatives....so if you had to bet on not the number in particular, but simply whether in the next drawing that you'd get a quad repetative or some other number it seems more likely that there will be a non-repetative number (.999 chance or 9990 possible combinations in 10000) as opposed to a repetative quad( a .001 chance or 10 in 10000) chance that their might be a quad
If you look at lotto drawings... for example the incidence of repetative quads in the PA state lottery since 1980 or about 6240 (52 weeks x 5 days x 24 years) drawings:

1111 10/6/92
2222 12/24/90

7777 12/28/03 11/3/89

8888 9/15/95

4444 3/15/04 mid day game which started Feb.2003

you get 5 incidences of it. 6235 of the 6240 drawings produced non repetative numbers or roughly a .999 percent occurance, vs 5 out of 6240 for quad repetatives or 8.01e-4

I think the reason that it seems and occurs less frequently is because of the small sampling - I guess by the laws of probability if this were to go on forever then they might even out over all...

does this make sense? sorry for being dense

thanks

 

[johnph77]

ajp -

Makes all the sense in the world to me. All the numbers are correct and your reasoning and conclusions are spot on. The only abnormality, however slight, is that there have only been five quads appear rather than the more statistically normal six.

gl

john