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Questions and Answers
Which of the following best describes the concept of events in probability theory?
Which of the following best describes the concept of events in probability theory?
- The intersection of all possible outcomes
- The entire sample space of a random experiment
- The probability of an outcome occurring
- Subsets of the sample space corresponding to specific outcomes or groups of outcomes (correct)
What is the sample space for rolling a fair six-sided die?
What is the sample space for rolling a fair six-sided die?
- {1, 2, 3, 4}
- {1, 2, 3, 4, 5}
- {1, 2, 3}
- {1, 2, 3, 4, 5, 6} (correct)
What does the Additivity Axiom state in probability theory?
What does the Additivity Axiom state in probability theory?
- $P(A∩B) = P(A) + P(B)$ for mutually exclusive events A and B
- $P(A∪B) = P(A) * P(B)$ for any events A and B
- $P(A∩B) = P(A) * P(B)$ for any events A and B
- $P(A∪B) = P(A) + P(B)$ for mutually exclusive events A and B (correct)
In probability theory, what does it mean for a probability to be non-negative?
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?
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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