Re: "Happens with Paobability 1"

On Aug 22, 1:30 pm, Sadeq <MSDou...@xxxxxxxxx> wrote:
What does this mean:

"Something happens with probability 1"

How does it differ from saying that something happans *certainly*?

Technically, probability 1 guarantees "almost certainty"
because there may be other allowed outcomes (with probability
0).

On a continuous distribution, every particular outcome
has zero probability. If you draw a random number from
a uniform distribution on [0,5], it is almost certain
that you won't draw a 3.0. The probability of outcomes
other than 3.0 is 1. The probability of drawing exactly
3.0 is zero.

Is this difference solely "theoretical," or there's also a "practical"
difference?

There's no practical difference I can think of. Indeed,
I think even for probabilities strictly less than 1
you can treat them as "1 for practical purposes". For
instance, I don't worry about suffocating in my office
due to the air molecules happening to take a random
configuration that leaves me in vacuum. That is an
event with nonzero probability, but one that really
doesn't worry me.

- Randy

.

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