Zak McGregor wrote:
>
>[clip]
>
> Actually, this is probably the only time I'll ever say this: Max is
> quite correct. The previous million rolls have no outcome on the fate of
> the next roll. Why? Well, because the chance of throwing 1 six is,
> unsuprisingly 1/6 (1 in 6). To do it twice is (1/6)^2, or 1/6*6 or 1/36.
> To roll a million consecutive sixes then is (1/6)^1 000 000. However,
> the next roll is still 1/6. The probability of getting 1 000 001 rolls
> of six in a row is (1/36)^1 000 001, but what we need to take into
> consideration is that you've already "used" (ie beaten the odds) on the
> first 1 000 000 throws. I hope I explained that OK... ;-/
This is correct re the million+1 roll (or any n+1 roll). But that is usually the question one is asking. Here's possibly an (outlandish) example to illustrate the more ususal question. We have two storerooms, one containing one million boxes. The other contains 1000 boxes. We can only enter one storeroom. One in every 100 boxes contains an antibiotic which we need in order to survive, and we must get it within the next (say) one hour. We need at least three doses. Which storeroom shall we search, or does it make no distance? Notice that we are _Not_ predicting the future but dealing with an already given but unknown state of affairs. It doesn't make any difference what the "odds" are on the next box containing the medicine but on the probability of some three boxes containing it of all those we open in the next hour.
Carrol