Nassim Nicholas Taleb says here

no probability that is 0 or 1 should ever change.

Despite these 6 questions

  1. Does an unconditional probability of 1 or 0 imply a conditional probability of 1 or 0 if the condition is possible?

  2. https://math.stackexchange.com/questions/1494682/is-it-correct-to-say-that-pa-1-to-pab-1-pa-1-to-pab-pa

  3. https://math.stackexchange.com/questions/1515756/is-a-probability-of-0-or-1-given-information-up-to-time-t-unchanged-by-informati

  4. Why does a probability of 0 or 1 remain unchanged with new information, intuitively?

  5. Is $E[1_A | \mathscr{F_t}] = 0 ~\text{or} ~ 1 \ \Rightarrow E[1_A | \mathscr{F_{s}}] = E[1_A | \mathscr{F_t}]$ is only almost surely?

  6. Prove/Disprove probability of 0 or 1 (almost surely) will never change and has never been different

It was pointed out to me in maths educator se that...

Actually, $P(A|B)=1$ does not imply $P(A)=1$ because $0 < P(A=B) < 1$.

  1. In fact I believe '$P(A|B)=1$' is equivalent to '$A \subseteq B$ a.s.' i.e. '$A^c \cap B = \emptyset$ a.s.' meaning $P(A^c \cap B)=0$ (where events are almost surely equal or subset/superset if the corresponding indicator random variables are almost surely, resp, $=$ or $\le$/$\ge$). Right?

  2. What's going on? NNT is wrong? Or NNT is right because e is referring to future information and replacing $B$ with $\Omega$ is actually the basic probability version of coarser partitions in filtrations in advanced probability i.e. past info instead of finer partitions in filtrations i.e. future info?

  • 4
    $\begingroup$ What exactly did NNT say and in what context? I got tired of trying to track through your long chains of links, never to land at a clear quotation, so for anyone without more patience than me, (2) is unintelligible. (1) is incorrect, BTW. Perhaps working with an elementary definition of conditional probability (that is, non measure-theoretic) will help make that clear. $\endgroup$
    – whuber
    Commented Jan 28, 2022 at 17:42
  • 2
    $\begingroup$ Consider choosing a random day of the week in some fashion, with each day being equally likely. Let $A$ = "chose a weekday" and $B$= "chose Wednesday". Clearly $P(A|B) = 1$ but $P(A)<1$. $\endgroup$
    – Glen_b
    Commented Jan 28, 2022 at 17:48
  • 2
    $\begingroup$ You are talking here about whether $P(A|B) =1$ implies $P(A) = 1$, but it seems like the rest of the questions you linked as well as the NNT quote are about whether $P(A) = 1$ implies $P(A|B) = 1$. $\endgroup$ Commented Jan 28, 2022 at 18:10
  • 1
    $\begingroup$ The probability "changing" refers to $P(A)$ "changing" into $P(A|B)$ once $B$ is known to be the case. Seems like you're very confused because you're interpreting it the wrong way round. $\endgroup$ Commented Jan 28, 2022 at 18:18

1 Answer 1


There is some ambiguity in what Nassim Nicholas Taleb (NNT) wrote.

Some chief executive was discussing the certainty of a future event. He said "the probability of [the event] happening is 100% now. But it could change in the future". The error is obvious.

Is the executive saying:

  1. "$P(A) = 1$, but if I get more knowledge (B) then $P(A|B) < 1$".

(this is impossible, and would seem to be the error he is indicating?)

or is the executive saying

  1. "$P(A|B_1) = 1$ (where $B_1$ is what I know about the present). Then it is possible that $P(A|B_2) < 1$ (where $B_2$ is what I know about some future time)"?

(This actually is possible. It also seems to be closer to what most people mean if they know $A$ is true with $100\%$ certainty: they really mean $P(A|B_1) = 1$ is true where $B_1$ is everything I know to be true right now).

It seems like your are interpreting NNT as saying the second thing is in error, and treating this as Gospel.

I am not sure that NNT had anything so precise in mind, but if he did it would seem to be the first interpretation.

I think there are also some philosophical issues with modeling people's belief systems using probability spaces. It might be a reasonable model, but I wouldn't make the mistake of confusing the model with reality. People are much more complex creatures than this.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.