Difference between Always and Probability 1
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In the comment section of this video:
Daniel Rui commented:
You used the words “never” and “always” synonymously with “probability 0” and “probability 1”, which I think gives less knowledgeable viewers the wrong impression. Other than that, fantastic presentation!
and in the following conversations columbus8myhw replied:
"Always" means every element of the sample space succeeds; "probability 1" means the measure of the set of succeeding elements equals the measure of the whole sample space.
Pick a real number uniformly from between 0 and 1. There is a probability 1 that it is irrational, but it's not always irrational as rationals exist.
English is not math.
