Questions and Answers
What is the difference between theoretical probability and empirical probability?
Empirical probability tells us how often an event occurs in an actual set of experiments or observations. Theoretical probabilities are based on theory telling us about events that occur indefinitely.
What does the Law of Large Numbers state?
The larger the number of individuals that are randomly drawn from a population, the more representative the resulting group will be of the entire population.
What are mutually exclusive events?
Events that cannot happen at the same time.
What are examples of mutually exclusive events?
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Probability is used to _____________.
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What is theoretical probability?
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What is empirical probability?
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Probability is always a value between ____ it may appear as a ____.
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If p(A) is 1, the event is certain to occur.
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If p(A) is 0, the event is certain not to occur.
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What are unusual events?
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What does the complement rule state?
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What is the addition rule of mutually exclusive events?
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What is the addition rule for not mutually exclusive events?
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For dependent events, what is the formula for conditional probability?
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In which context is the word 'given' used?
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In which context is the word 'or' used?
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What are independent events?
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What is a permutation?
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In permutations, what is the significance of order?
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In combinations, what is the significance of order?
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How do you find the area to the right in a standard normal distribution curve?
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How to find the area between in a normal distribution curve?
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How to find the z score when given area to the right or to the left?
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In what context are area, proportion, and probability considered the same?
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What is the z score of x?
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When looking for an area that is greater, which direction are we looking?
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To find the area to the right, what must we subtract?
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How do we find the value if we know the mean, standard deviation, and z score?
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What does the Central Limit Theorem state?
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What is the formula for the Central Limit Theorem?
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Study Notes
Probability Concepts
- Theoretical Probability: Derived from theoretical understanding, indicating long-run relative frequencies of events.
- Empirical Probability: Based on actual experiments or observations, showing how often an event occurs in practice.
- Probability values range between 0 (impossible event) and 1 (certain event); can be expressed as a fraction, decimal, or percentage.
Rules of Probability
- Law of Large Numbers: Sample sizes increase, results become more representative of the population's true probabilities.
- Complement Rule: P(A^c) = 1 - P(A); the probability of an event not occurring is equal to one minus the probability it will occur.
- Addition Rule for Mutually Exclusive Events: P(A or B) = P(A) + P(B); for events that cannot happen simultaneously.
- Addition Rule (Not Mutually Exclusive): P(A or B) = P(A) + P(B) - P(A and B) applies when events can occur together.
Types of Events
- Mutually Exclusive Events: Events like turning left or right, or getting heads or tails, cannot occur at the same time.
- Independent Events: Events where the occurrence of one does not affect the other, calculated as P(A or B) = P(A) + P(B).
- Dependent Events: The occurrence of one event depends on another; use P(A and B) with P(B/A) for calculations.
Unusual Events
- Defined as events happening less than 5% of the time, indicating rarity.
Statistical Measures
- Z Score: Calculated as (score - mean) / standard deviation; indicates the number of standard deviations an observation is from the mean.
- Area proportions in normal distribution are equivalent to probabilities; finding areas involves using Z scores and charts.
Sampling and Distribution
- Central Limit Theorem: As sample size (n) increases (n > 30), the sampling distribution of the mean approaches a normal distribution.
- Finding areas in standard normal distributions requires reference to Z charts; to find the area to the right, subtract the area from 1.
Permutations and Combinations
- Permutation: The arrangement or ordering of R objects chosen from a total of n, where order is significant.
- Combination: Selection of R objects from n where order does not matter, focusing on the grouping rather than arrangement.
Finding Areas and Values
- To find the area between two Z scores, look up each score, subtract the smaller area from the larger for the final value.
- To find associated values given the mean and standard deviation, use the formula x = mean + (z * standard deviation).
Summary
- Probability theories and rules form the foundation of understanding random events and their behaviors.
- Becoming proficient in calculating and interpreting probabilities enhances comprehension in statistics.
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Explore key concepts in statistics with these flashcards, focusing on the difference between theoretical and empirical probability, as well as the Law of Large Numbers. Perfect for preparing for your upcoming statistics test.