Questions and Answers
Which of the following best describes the concept of events in probability theory?
Subsets of the sample space corresponding to specific outcomes or groups of outcomes
What is the sample space for rolling a fair six-sided die?
{1, 2, 3, 4, 5, 6}
What does the Additivity Axiom state in probability theory?
$P(A∪B) = P(A) + P(B)$ for mutually exclusive events A and B
In probability theory, what does it mean for a probability to be non-negative?
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If event A and event B are not mutually exclusive, what is the formula for the probability of their union?
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Study Notes
Probability Theory Basics
- In probability theory, an event is a set of outcomes of an experiment.
Sample Space
- The sample space for rolling a fair six-sided die is the set of all possible outcomes: {1, 2, 3, 4, 5, 6}.
Additivity Axiom
- The Additivity Axiom states that for any countable sequence of disjoint events, the probability of the union of the events is equal to the sum of their individual probabilities.
Non-Negative Probability
- In probability theory, a probability is non-negative if its value is greater than or equal to 0, i.e., 0 ≤ P(event) ≤ 1.
Probability of Union
- If event A and event B are not mutually exclusive, the formula for the probability of their union is: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
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