I'm looking for the 'mathematical' symbol, if it exists, that denotes 'equally likely'. For example, one has two potential outcomes from a present state, both of which are equally likely (or probable). Is there a symbol for that?

  • 4
    $\begingroup$ Won't "$=$" do, when suitably applied? $\endgroup$
    – whuber
    Feb 24 '21 at 19:21
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    $\begingroup$ I agree with @whuber. You usually see P(outcome A | current state) = P(outcome B | current state). It is more of a mathematical statement than a symbol. $\endgroup$
    – R Carnell
    Feb 24 '21 at 19:55
  • $\begingroup$ @RCarnell, why not turn your comment into an official answer? That way this thread won't count as unanswered. $\endgroup$ Apr 22 '21 at 8:19
  • $\begingroup$ Couple distinctions: are the two outcomes complementary like heads versus tails on a fair coin? Also you mention "state", is this actually a dynamical system state (that is otherwise random) or more simply an assumption (like that the coin is in fact fair)? $\endgroup$
    – AdamO
    Apr 23 '21 at 17:55

In statistics we normally say

$$P(\text{Event A} | \text{current state}) = P(\text{Event B} | \text{current state})$$ to denote outcomes that are equally probable.

  • $\begingroup$ Actually, probabilities are assigned to events rather than outcomes. $\endgroup$
    – whuber
    Apr 23 '21 at 13:18
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    $\begingroup$ Edited. In some ways, outcomes are a specific type of event. I like the more general "event". $\endgroup$
    – R Carnell
    Apr 23 '21 at 16:28

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