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statisticsprobabilityprobability-theory

Probability of occuring of An infinitely often

IF probability of occurance of A , infinitely often is 0, does it mean probability of occurance of A complement , infinitely often is 1???

Solution

  • The opposite of A occurring infinitely often is not 

    'not A' occurring infinitely often

    but 

    'A' not occurring infinitely often

    i.e. 

    'A' occurring only a finite number of times.

    As Mark pointed out, the meaning of this for not A depends on whether you have a finite number of trials ('occurrences') or not:

    • finite number of trials: also not A can only occur a finite number of times

    • infinite number of trials: A only occurs for a finite number of trials, so not A occurs for the rest of the trials which are infinitely many (assuming only A and not A can occur in each trial).