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# Thread: Math - probablity question

1. ## Math - probablity question

&lt;sigh&gt; it's been 30 years or so since I've done this and I'm drawing a blank.

What are the odds of a supposedly random event:
that happened 5 times
that happened on a Saturday each of those 5 times
over 2 years.

Intuitively I know this is virtually impossible, the odds must be astronomical, but some people just have to have some numbers to finally convince them...

2. ## Re: Math - probablity question

If it's truly random,
and the events are not dependent on each other,
and the only variable here is on which day of the week the event occurs

then it appears that the likelihood of the event taking place on 5 Saturdays, rather than any other day is

1/7 * 1/7 * 1/7 * 1/7 * 1/7

right?

Is that astronomical? It's hard to say without some context. Certainly it's the same as "5 Tuesdays", or the same as the sequence "Monday, Tuesday, Wednesday, Thursday, Friday".

And certainly the odds for it happening next on a Saturday are still just 1/7, given the same assumptions.

(Now often, on further investigation, the event isn't truly random, or once established is periodic. In those cases, the math does not apply)

3. ## Re: Math - probablity question

Sorry for the confusing context, this should make it clearer.
Here is the situation.
A script runs once every day .
The script has failed 5 times.
Each time it was on a Saturday.

True, the odds are 1/7 that the next time will be a Saturday, but I'm asking what are the odds that this is truly random given that this has run 730 times (2 years), failed 5 times - and each time on a Saturday? Are the odds 1/16807 no matter how many years? That can't be right.

4. ## Re: Math - probablity question

I suspect you are correct - there is probably a definite cause and it is not random.

And if it is not random, then odds aren't relevant.

5. ## Re: Math - probablity question

David,

Are you wanting to 1) calculate the odds, 2) get ideas on how to get at root cause, or 3) both?

Here is one resource:
http://en.wikipedia.org/wiki/Binomial_distribution

6. ## Re: Math - probablity question

Just the odds. I want to first prove that it is virtually impossible that this is "random".

7. ## Re: Math - probablity question

[img]/images/graemlins/smile.gif[/img] Even if you calculate the odds which will never be zero - what do you gain?

Are these Saturdays unique relative to holidays and/or business cycles such as end-of-month processing?

8. ## Re: Math - probablity question

How long does the script take to run and what type of failure occurs? Is it dependent on the Inter, or intra net? What is the mean time between failures?

9. ## Re: Math - probablity question

x = number of possibilities during time period
q = total time period
n = number of occurrences

(x/q)^n

So in this formula we have 104 possible days out of a total of 730 days where it could occur on a saturday and each of the 5 times it occurred was on a Saturday.

(104/730)^5
or
(52/365)^5= .000058688417057480754356176255798719

1/.000058688417057480754356176255798719 = 17,039.

So your odds are roughly 1 in 17,039. Not exactly astronomical. You should focus more on demonstrating the pattern and finding out what else was going on on those saturdays. Antivirus scans? Software releases pushed out across network?

10. ## Re: Math - probablity question

Thanks All.

And apologies about my vagaries, the issue/data/problem is sensitive and I couldn't reveal much.

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