Question

Fill in the blank

if s is the sample space of a random experiement and e is any event, the axioms of probability are:

Answer 1

The axioms of probability relate to the probability of events in a sample space. The axioms are as follows: 1) The probability of an event is always greater than or equal to 0. 2) The probability of the entire sample space is 1. 3) If events are mutually exclusive, then the probability of their union is the sum of their individual probabilities.

Step-by-step explanation:

The axioms of probability relate to the probability of events in a sample space. The axioms are as follows:

1. Axiom 1: The probability of an event E is always greater than or equal to 0, that is, P(E) ≥ 0.
2. Axiom 2: The probability of the entire sample space S is 1, that is, P(S) = 1.
3. Axiom 3: If E1, E2, E3, ... are mutually exclusive events, meaning they have no outcomes in common, then the probability of the union of these events is equal to the sum of their individual probabilities, that is, P(E1 ∪ E2 ∪ E3 ∪ ...) = P(E1) + P(E2) + P(E3) + ...

For example, if you have a sample space of tossing a fair coin, the probability of getting heads (event H) would be P(H) = 0.5, and the probability of tails (event T) would also be P(T) = 0.5. And since H and T are mutually exclusive events, the probability of getting either heads or tails would be P(H ∪ T) = P(H) + P(T) = 0.5 + 0.5 = 1.