Podcast
Questions and Answers
The forecast is 70% chance of rain today. So, take my ______
The forecast is 70% chance of rain today. So, take my ______
umbrella
It’s cloudy, it may rain. So, take my ______
It’s cloudy, it may rain. So, take my ______
umbrella
Objective Probability is based on ___________ data.
Objective Probability is based on ___________ data.
Quantitative
Subjective Probability is based on ___________ experiences.
Subjective Probability is based on ___________ experiences.
Mutually exclusive events have ___________ outcomes on any one trial.
Mutually exclusive events have ___________ outcomes on any one trial.
Collectively exhaustive events list all ___________ outcomes.
Collectively exhaustive events list all ___________ outcomes.
Two dice are rolled, find the probability that the sum is equal to 1: 0/36 or ___________
Two dice are rolled, find the probability that the sum is equal to 1: 0/36 or ___________
Two dice are rolled, find the probability that the sum is equal to 4: 3/36 or ___________
Two dice are rolled, find the probability that the sum is equal to 4: 3/36 or ___________
A die is rolled, and a coin is tossed, find the probability that the die shows an odd number, and the coin shows a ___________
A die is rolled, and a coin is tossed, find the probability that the die shows an odd number, and the coin shows a ___________
Bayesian Theorem is used to calculate ___________ probability.
Bayesian Theorem is used to calculate ___________ probability.
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Study Notes
Probability Concepts
- Mutually exclusive events: cannot occur simultaneously
- Non-mutually exclusive events: can occur simultaneously
- Statistically independent events: occurrence of one event does not affect the probability of another event
- Statistically dependent events: occurrence of one event affects the probability of another event
Marginal and Joint Probability
- Marginal probability: probability of an event occurring (e.g., P(A))
- Joint probability: probability of two or more events occurring at the same time (e.g., P(A and B))
- Conditional probability: probability of an event occurring given that another event has occurred (e.g., P(A|B))
Bayesian Theorem
- Bayes' Theorem: used to update probabilities based on new information
- Formula: P(A|B) = P(B|A) x P(A) / P(B)
- Posterior probability: revised probability after considering new information
- Prior probability: initial probability before considering new information
Example Problems
- Probability of two girls given at least one girl: 1/3 or 0.33
- Probability of a fair die given a roll of 3: 0.22
- Probability of a loaded die given a roll of 3: 0.78
Fair and Loaded Dice
- Fair assumption: uniform or equal prior probabilities assigned to all hypotheses
- Loaded die: non-uniform probabilities assigned to outcomes
- P(Fair) = 0.50, P(Loaded) = 0.50
- P(3|Fair) = 0.166, P(3|Loaded) = 0.60
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