Question

If S is the sample space of a random experiment and E is any event, the axioms of probability are:

A.) P(S) = 1

B.) 0 ≤ P(E)

C.) For any two events with E1, E2 with E1 and E2 = 0, P(E1 or E2) = P(E1)+P(E2)

D.) All of the choices are correct

E.) None of the choices is correct

Answer 1

The second axiom of probability is that the probability of the entire sample space is one. Symbolically we write P(S) = 1, so A.) is correct

The first axiom of probability is that the probability of any event is a non negative real number i.e. 0 ≤ P(E), so B.) is correct

The third axiom of probability deals with mutually exclusive events. If E₁ and E₂ are mutually exclusive, meaning that they have an empty intersection then P(E₁ U E₂ ) = P(E₁) + P(E₂), so C.) is correct

So correct answer is D.) All of the choices are correct