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Probability is an attempt to treat uncertainty in a most rational way.

We use probability as intractability metrics -- measuring how difficult would it be for our adversary to compromise our system in a timely manner.

We use probability to rate our security measures. If a security measure reduces the chance for a successful hacking of our system from, say 25% to, 5% -- then the measure is advisable (provided it does not cost too much...)

External Links:

classic probability in detail

popular probability math video.

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