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Questions and Answers
What is the set of all possible outcomes of an experiment?
What is the set of all possible outcomes of an experiment?
What is the probability of the sample space?
What is the probability of the sample space?
What is the formula for the probability of the complement of an event?
What is the formula for the probability of the complement of an event?
What type of probability is based on the number of favorable outcomes and the total number of possible outcomes?
What type of probability is based on the number of favorable outcomes and the total number of possible outcomes?
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What is the type of event where the occurrence of one event does not affect the probability of another event?
What is the type of event where the occurrence of one event does not affect the probability of another event?
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What type of random variable can take on only specific, distinct values?
What type of random variable can take on only specific, distinct values?
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What is a table or formula that describes the probability of each possible value of a discrete random variable?
What is a table or formula that describes the probability of each possible value of a discrete random variable?
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What is a function that describes the probability of a continuous random variable taking on a certain value or range of values?
What is a function that describes the probability of a continuous random variable taking on a certain value or range of values?
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Study Notes
Basic Concepts
- Experiment: An action or situation that can produce a set of outcomes.
- Sample Space: The set of all possible outcomes of an experiment.
- Event: A subset of outcomes of an experiment.
- Probability: A measure of the likelihood of an event occurring.
Probability Rules
- Probability of an Event: A number between 0 and 1 that represents the likelihood of an event occurring.
- Probability of the Sample Space: 1 ( certainty)
- Probability of the Empty Set: 0 (impossibility)
- Complementary Probability: P(A') = 1 - P(A)
- Addition Rule: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
- Multiplication Rule: P(A ∩ B) = P(A) × P(B)
Types of Probability
- Theoretical Probability: Based on the number of favorable outcomes and the total number of possible outcomes.
- Experimental Probability: Based on the results of repeated trials.
- Conditional Probability: The probability of an event occurring given that another event has occurred.
Independent and Dependent Events
- Independent Events: The occurrence of one event does not affect the probability of another event.
- Dependent Events: The occurrence of one event affects the probability of another event.
Random Variables
- Discrete Random Variable: A random variable that can take on only specific, distinct values.
- Continuous Random Variable: A random variable that can take on any value within a certain range or interval.
Probability Distributions
- Discrete Probability Distribution: A table or formula that describes the probability of each possible value of a discrete random variable.
- Continuous Probability Distribution: A function that describes the probability of a continuous random variable taking on a certain value or range of values.
Basic Concepts
- An experiment is an action or situation that can produce a set of outcomes.
- A sample space is the set of all possible outcomes of an experiment.
- An event is a subset of outcomes of an experiment.
- Probability is a measure of the likelihood of an event occurring.
Probability Rules
- Probability of an event is a number between 0 and 1 that represents the likelihood of an event occurring.
- The probability of the sample space is 1, representing certainty.
- The probability of the empty set is 0, representing impossibility.
- The complementary probability of an event A is 1 - P(A).
- The addition rule for probability is P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
- The multiplication rule for probability is P(A ∩ B) = P(A) × P(B).
Types of Probability
- Theoretical probability is based on the number of favorable outcomes and the total number of possible outcomes.
- Experimental probability is based on the results of repeated trials.
- Conditional probability is the probability of an event occurring given that another event has occurred.
Independent and Dependent Events
- Independent events are events where the occurrence of one event does not affect the probability of another event.
- Dependent events are events where the occurrence of one event affects the probability of another event.
Random Variables
- A discrete random variable is a random variable that can take on only specific, distinct values.
- A continuous random variable is a random variable that can take on any value within a certain range or interval.
Probability Distributions
- A discrete probability distribution is a table or formula that describes the probability of each possible value of a discrete random variable.
- A continuous probability distribution is a function that describes the probability of a continuous random variable taking on a certain value or range of values.
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Description
Test your understanding of basic concepts in probability, including experiments, sample spaces, events, and probability rules.
