10 Questions
The forecast is 70% chance of rain today. So, take my ______
umbrella
It’s cloudy, it may rain. So, take my ______
umbrella
Objective Probability is based on ___________ data.
Quantitative
Subjective Probability is based on ___________ experiences.
Personal
Mutually exclusive events have ___________ outcomes on any one trial.
one
Collectively exhaustive events list all ___________ outcomes.
possible
Two dice are rolled, find the probability that the sum is equal to 1: 0/36 or ___________
0%
Two dice are rolled, find the probability that the sum is equal to 4: 3/36 or ___________
8.33%
A die is rolled, and a coin is tossed, find the probability that the die shows an odd number, and the coin shows a ___________
head
Bayesian Theorem is used to calculate ___________ probability.
Conditional
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
Test your knowledge on basic probability aspects such as addition of mutually exclusive and non-mutually exclusive events, statistically independent and dependent events, marginal/simple probability, joint probability, conditional probability, as well as Bayesian Theorem. Explore how Bayes' theorem is used to incorporate additional information in probability calculations.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
