Quote (iLuxxy @ Feb 16 2013 09:37am)
Your math will add up to 100% chance to drop eventually.
Whereas its impossible to guarantee a drop, no matter how many times you run it, because previous results do not affect the future.
Actually the equation only guarantees a drop if you do it an infinite number of times.
The limit as x approaches infinity of 1-(1-0.0003)^x = 1
If you do it an infinite number of times the chance of success will be 100%, for any finite number of times it will be less than 100%.
The probability of getting all failures (Pf) + probability of not getting all failures (Ps) = 100%
Pf + Ps = 1
Pf = (1- 0.0003)^n = (0.9997)^n
Plugging that in to the equation above:
(0.9997)^n + Ps = 1
solve for Ps:
Ps = 1 - (0.9997)^n
probability of not getting all failures = probability of one or more successes = Ps = 1 - (0.9997)^n
Quote (iLuxxy @ Feb 16 2013 01:12pm)
It doesn't matter how many times you do it.
Each time it's 0.03% chance to drop.
Yes, the probability of 'getting lucky' on any individual run is 0.0003 and that is what the equation models.
Think about it in a simpler case. Flipping a coin. You have a 50% chance to get heads on any given flip. Lets consider the probability of getting 1 or more heads in 10 flips.
Pf + Ps = 1
Pf = (1 - .5)^10
(1 - .5)^10 + Ps = 1
Ps = 1 - (1 - .5)^10
Ps ≈ 0.999 ≈ 99.9%
While the chance of getting a heads on any given flip is still only 50%, the chance of getting 1 or more heads in 10 flips is almost 100%. It will never be 100% unless you do an infinite number of flips.
This is not the gamblers fallacy. The gamblers fallacy would be to wait until you had done 5 of the 10 flips (and not having received a heads yet), then using the formula above with n = 10 for the last remaining 5 flips. The correct method would be to use n=5.
So in that situation (after 5 failed flips) someone using the gamblers fallacy would say you have 99.9% chance to get heads in the next 5 flips. Calculating it correctly it would be 96.9% chance.
This post was edited by Azrad on Feb 16 2013 03:14pm