To tell a bit of my background, I'm supposed to graduate from a business polytechnic within a year, so obviously fumbling like this with statistical math is a bit of an embarrassment. So, I decided to redeem myself by figuring the correct formula that'll arrive to that number. It's 39/7 times 38/6 times [...] 33/1. To learn is to find solutions to the mistakes one makes.
BTW, your original number is known as "39 permute 7". The other number is "39 choose 7" or "39 combine 7". So, do you know what "39 choose 32" would be equal to?
But here's the catch: the record is only guaranteed to approach the theoretical value, not reach it or balance around it.
You are misunderstanding. The probability of getting within a set distance from the true mean approaches 1. But that doesn't mean that the sample mean is guaranteed to approach the true mean.
I remember this example from an episode of Numb3rs. Maybe I should start watching that again?
The answer to the Monty Hall problem is "it depends". If someone doesn't know that, or understand what it depends on, one can make a lot of money off of them.
Well, the odds of it not coming up in one game are 15,380,936 / 15,380,937 or 0.999999934984455. So, assuming one game per week, the odds of the number not coming up in 50 years is 0.999999934984455^(50*52) = 0.999830974. That makes the odds of it coming up in 50 years 1 - 0.999830974 = 0.000169026 or roughly 1 in 5916. This is assuming Excel hasn't made any rounding errors.
There's actually another way to calculate it: multiply 1 by 50 by 52, divide by 15,380,936, then multiply by -1. Finally, put that number into Excel's exp() function.
This doesn't give the exact answer; it gives an approximation. But for large numbers, it's very accurate (in this case, it gives .999830974 as well), and calculating it your way will require approximation, anyway. Plus, if you ever find yourself with nothing but a slide rule, you can use my formula. In fact, if you get good at it, you can calculate a good approximation in your head.
Before any bias occurs, however, we can say that in a sufficiently long series of trials, strings of bias will be equally likely to occur either way.
But that statement is either true for any series of trials, even short ones, or true of none of them. If you flip a coin twice, you're just as likely to get 2 heads as to get 0.
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