|Posted: September 4, 2007, 4:59 pm - IP Logged|
Sorry, dog ate my work.
Oh, wait... here we go.
Probability of 8 doubles in a row: (270 / 1000) ^ 8 = 0.0000282429536481
Probability as a fraction of 1 to the nearest positive integer denominator: 0.0000282429536481 = 1 / (1 / 0.0000282429536481) ≈ 1 / 35,407
Probability then becomes approximately: 1 in 35,407
The denominator is also approximately the same as average rate of reoccurrence: 35,407 average units of measure between occurrences
Unit of measure is 1 day, 35,407 x 1 day = 35,407 days
Convert to years and days, 1 year = 365.2425 days, years = days / number of days in a year = 35,407 days / 365.2425 days per year = 96.9410734 years. Take fractional part by subtracting integer value of 96.9410734, 96, then multiply by 365.2425 days per year to get remaining days, 0.9410734 year x 365.2425 days per year ≈ 344 days. Time between occurrences, 96 years 344 days.
Potential reoccurrence probability is e -(1 / 35407) ≈ .999971757 or 99.9971757%, but keep in mind the potential occurrence probability balances it by 1 - e -(1 / 35407) ≈ 0.000028242602 or 0.0028242602%
The all states aspect I'll not get into... just figure total number of draws per year both midday and evening and divide into 35,407 to get a yearly average rate of reoccurrence across the board. It may have happen in recent past, but for which lottery I know not.
Presented 'AS IS' and for Entertainment Purposes Only.
Any gain or loss is your responsibility.
Use at your own risk.
Order is a Subset of Chaos
Knowledge is Beyond Belief
Wisdom is Not Censored
Douglas Paul Smallish
US God plus Islam Allah