Yes. When I have played the lottery for the lols, I bet on 6 numbers in one 10 number set, all of them over 31 to avoid the players who pick numbers based on birthdays, so that if I win I statistically have the best chance of winning the best share of the winnings.
That's because people don't bet on 6 numbers within the same 10 gap, again thinking it's unlikely that 6 numbers within the 40's or something is any less likely to come up than 6 other random numbers.
Whether those numbers have ever one before is irrelevant in that decision.
No idea what you're talking about with that one.
Agreed, it only works for events which are independent. Two plane crashes are independent for the most part, unless it's a bad runway, or a particular fault that exists across 10 aircraft etc that causes the crash.
http://en.wikipedia.org/wiki/Independence_(probability_theory)
Your lungs working now and in 10 minutes are not independent events. Your lungs working in 10 minutes time is dependent on them working now.
The chances of that happening as you've stated there are close to zero, but not because it's already happened.
They're close to zero because the probability of that happening even in the first place was miniscule.
The fact it's already happened however does not change the chance of it happening within the next 30 days again, unless the two events are in some way dependent. (E.g. it was a fault across all of that particular model of plane, or the runway isn't suitable for that type of plane, etc)
The airline industry takes a heck of a long time to do anything. First you'll have the equivalent of the NTSB in the country doing their investigation to confirm the cause of the crash (if it's particularly obvious that it's a plane fault, they might ground all of that particular model of plane during the investigation period), they'll then issue a notice if they believe that it was caused by a plane malfunction/bad maintenance and advise airlines to do something. The airlines will then do something over several months-years to rectify the problem.
The airlines react very slowly, because they can't just ground their fleets and do maintenance works/checks on them without going bankrupt.
With regards to roulette, it's the famous case in monte carlo that pretty much defines the gambler's fallacy:
After a black comes up, there's a 50% chance a black will come up, and a 50% chance a red will come up. A black coming up previously has no bearing on whether there'll be another black come up in the next spin.
A plane crashes somewhere in the world, and the chance of another one crashing tomorrow is exactly the same (ignoring differences in flight volumes, etc). Just because one crashed today doesn't mean one can't crash tomorrow because it's a rare event. Whilst the combined probability of two plane crashes in one month is very low, once one of the crashes has already occurred the probability of the second crash is exactly the same as it is for the first crash before that one happened, unless there is some kind of serious fault in that model of plane which means that all of them are liable to crash or something within the next week.
Which of the following do you disagree with?
The chance of a major airline plane crashing somewhere in the world in one month is low, lets go with a completely made up 5%.
The chance of 2 planes crashing in any 30 days, given our 5% chance of a major airline plane crashing anywhere in the world in one month assumption is 0.05x0.05 or 0.25% (5% x 5%).
We've agreed the chance of a plane crashing anytime in a 30 day window is 5%, so the chance of a second plane crashing after the first plane in the next 30 days is also 5%. This means that a plane crashing in next 30 days is just as likely as it was before the first crash.
Whilst the chance of two planes crashing in a 30 day window is much smaller than the chance of one plane crashing in 30 days
before a plane has crashed, once the first plane has crashed, the chance of a plane crashing is exactly the same as it was before the crash, i.e. 5%.
I'm not sure what there is to not get about that?
Unless you're arguing that worldwide plane crashes are not independent events but are all dependent events. (i.e. one plane crash happening in Miami means a plane crash in Sydney is more or less likely.. because they are in some way linked, all planes have fault engines, all runways are built badly, or that all the airlines will somehow fix all the problems with existing planes in the next 30 days because of this crash etc)
