Posted by Jope on Tuesday, August 26, 2008 at 10:07pm.
We can say that the value of p is bounded above by 1 and below by 0. An event can not have greater than a 100% chance of occurring, nor can it have less than a 0% chance of occurring, hence its boundary conditions of [0,1].
Given this, there are two possible outcomes. Occurring or not occurring. Since we know the probability of the event occurring is p, which is bounded above by 1; the probability of the event not occurring must be (1-p).
Alternatively, for lack of a better way of putting it, p can not occur and not occur at the same time. So the probabilities of p occurring and not occurring must add up to one.
Good luck, hope that helps :)
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