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Questions and Answers
What is the formula for theoretical probability?
What is the formula for theoretical probability?
What is the range of values for a probability?
What is the range of values for a probability?
What is the rule of probability that states the probability of an event and its complement add up to 1?
What is the rule of probability that states the probability of an event and its complement add up to 1?
What is the type of event where the occurrence of one event affects the probability of the other event?
What is the type of event where the occurrence of one event affects the probability of the other event?
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What is the formula for conditional probability?
What is the formula for conditional probability?
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What is a probability distribution?
What is a probability distribution?
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What is the probability of two or more independent events?
What is the probability of two or more independent events?
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What is the probability of an impossible event?
What is the probability of an impossible event?
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Study Notes
Probability
Definition
- Probability is a measure of the likelihood of an event occurring.
- It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
Experimental Probability
- Experimental probability is the probability of an event occurring based on the results of an experiment.
- It is calculated as the number of times the event occurs divided by the total number of trials.
Theoretical Probability
- Theoretical probability is the probability of an event occurring based on the number of favorable outcomes divided by the total number of possible outcomes.
- It is calculated using the formula: P(E) = Number of favorable outcomes / Total number of possible outcomes
Rules of Probability
- The probability of an event is always between 0 and 1.
- The probability of an impossible event is 0.
- The probability of a certain event is 1.
- The probability of an event and its complement (the event not occurring) add up to 1. P(E) + P(E') = 1
- The probability of two or more independent events is the product of their individual probabilities. P(A and B) = P(A) × P(B)
Types of Events
- Independent Events: Events where the occurrence of one event does not affect the probability of the other event.
- Dependent Events: Events where the occurrence of one event affects the probability of the other event.
- Mutually Exclusive Events: Events that cannot occur at the same time.
- Exhaustive Events: Events that include all possible outcomes of an experiment.
Conditional Probability
- Conditional probability is the probability of an event occurring given that another event has occurred.
- It is calculated using the formula: P(A|B) = P(A and B) / P(B)
Probability Distribution
- A probability distribution is a table or graph that shows the probability of each possible value of a random variable.
- It is used to visualize and analyze the probability of different outcomes.
Definition of Probability
- Probability quantifies the likelihood of an event, expressed as a value between 0 and 1.
- A probability of 0 denotes an impossible event, while a probability of 1 signifies a certain event.
Experimental Probability
- Experimental probability arises from conducting experiments and analyzing results.
- Calculated by dividing the number of times an event occurs by the total number of trials conducted.
Theoretical Probability
- Theoretical probability is determined through mathematical calculation based on possible outcomes.
- Formula: P(E) = Number of favorable outcomes / Total number of possible outcomes.
Rules of Probability
- Probabilities lie exclusively within the range of 0 to 1.
- An impossible event has a probability of 0, while a certain event has a probability of 1.
- The sum of the probabilities of an event and its complement equals 1: P(E) + P(E') = 1.
- For independent events, the overall probability is the product of their individual probabilities: P(A and B) = P(A) × P(B).
Types of Events
- Independent Events: Events that do not influence each other's occurrence.
- Dependent Events: Events where the occurrence of one changes the likelihood of the other.
- Mutually Exclusive Events: Events that cannot occur simultaneously.
- Exhaustive Events: A complete set of outcomes for an experiment.
Conditional Probability
- Conditional probability assesses the likelihood of an event given that another related event has occurred.
- Calculated using the formula: P(A|B) = P(A and B) / P(B).
Probability Distribution
- A probability distribution presents a comprehensive view of the probabilities for all potential values of a random variable.
- Aids in the visualization and analysis of varying outcomes in probability scenarios.
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Test your understanding of probability, including experimental and theoretical probability. Learn how to calculate probability and more!
