Quote:
Originally Posted by jdunford In fact, I'd argue that it is "infinitely more probable", given the other bins are finite... |
Just because the other possibilities are finite in timespan and the last one is not does NOT make them 'infinitely more probable'
Why?
The total probability of all the options added together are 100% (by design). If the first 5 options have a combined probability > 0 then we know that the last option has a probability < 100%
Mathematically:
Per definition:
P(option 1-5) >= 0
P(option 6) >= 0
P(1-5) + P(6) = 100%
Assumption:
P(1-5) > 0 (we assume there is a non-zero chance that chips will arrive this year)
Proof that P(6) is not infinitely more likely than P(1-5):
Proof by counter-example
Let R be how much more likely P(6) is than P(1-5)
thus R = P(6) / P(1-5)
if we set: R = oo (infinity)
then: oo = P(6) / P(1-5)
which means that either
1) P(6) = oo
2) P(1-5) = 0
But we know 1) to be false because P(6) cannot be more than 100% (per definition) and we know 2) to be false (assumption 1)
QED