When we roll a dice the probability of getting each number is (1/6). Apart from the fact that probabilities are supposed to be in the range of 0-1; why do they all add up to 1?
In: 3
Because the results are mutually exclusive and comprehensive.
Mutually exclusive means that you can’t get more than one result. When you roll a die, it only shows one face. You can’t roll a 1 and a 2 simultaneously.
Comprehensive means it includes all possible outcomes. When you roll a die, it has to show one of the faces. It can’t show no face, or some other possibility.
If the possible outcomes were not mutually exclusive then the probabilities could add up to something greater than 1, because some outcomes could get double-counted.
If the possible outcomes aren’t comprehensive then the probabilities could add up to something less than 1, because some outcomes wouldn’t get counted at all.
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