Questions and Answers
What is the definition of a sample space?
The set of all possible outcomes, with mutually exclusive and collectively exhaustive elements
What are the axioms of probability?
$P(A) extgreater= 0$, $P(A_i)P(B extbar A_i) extless extgreater j P(A_j)P(B extbar A_j)$, $P(A extintercal B) = P(A)P(B)$
What is the corollary related to independent events?
If A and B are independent, then A and $B^c$ are independent
What is the probability of the empty set?
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How is the probability of a union of disjoint events calculated?
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Study Notes
Sample Space and Probability Axioms
- A sample space is a set of all possible outcomes of an experiment, denoted by Ω (Omega) and is usually represented by the set of all possible outcomes.
Axioms of Probability
- The probability of an event is a non-negative real number, denoted by P(E) ≥ 0.
- The probability of the sample space is equal to 1, P(Ω) = 1.
- The probability of the union of a countable number of disjoint events is the sum of their individual probabilities.
Independent Events
- The corollary of independent events states that if A and B are independent events, then P(A ∩ B) = P(A) × P(B).
Empty Set and Union of Disjoint Events
- The probability of the empty set is 0, P(∅) = 0.
- The probability of a union of disjoint events A and B is calculated by P(A ∪ B) = P(A) + P(B).
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