We want to select the statements that are axioms of probability.
We will see that the correct options are C, D, and E.
The easier thing to do, is writing the axioms and see which statements relate to those.
The axioms of probability are:
The probability of an event is a non-negative real number and equal to or smaller than 1. The probability of one of all the possible events to happen is 1, this also means that the sum of all the probabilities of the individual events is equal to 1.The probability (assuming additivity) of one event or other happening is equal to the sum of the probabilities.
Now that we know the axioms, let's see if the statements relate to them or not.
A) The probability of two events occurring is always greater than 0.
false, if we take two events with a probability of zero, then the probability of these two events occurring is zero.
B) The probability of an event A is the number of outcomes in A divided by the number of outcomes in the sample space.
This is false, this is only true when all the outcomes in the sample space have the same probability of happening.
C) The probability of an event is a number that is at least 0 and no more than 1.
True, by the first axiom.
D) If two events A and B are mutually exclusive (disjoint), then P(A or B)=P(A)+P(B).
True, related to the third axiom, disjoint events are additive.
E) The combined probability of all possible outcomes is equal to 1.
True, by the second axiom.
so the correct options are C, D, and E.
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