probability Flashcards
What are some examples of how probability is used in everyday life?
- Weather (chance of rain)
- Gambling/betting/lottery
- Advertising (algorithm-based ad recommendations)
- Spotify playlists (suggesting artists)
What is deterministic theory in science?
A theory where outcomes are fully determined by initial conditions with no randomness, and observations must be consistent with the theory.
Give an example of a deterministic theory
Einstein’s theory of general relativity: The gravity of large objects can bend light, and the position of stars should be displaced when observed near the sun.
What is probabilistic theory in science?
A theory where outcomes are described by probabilities, allowing for randomness and uncertainty.
How does probability play a role in psychology?
Probability helps us determine what behaviors are more likely and assists in hypothesis testing by identifying patterns in data and identifying unlikely events as evidence.
What are the three types of probability?
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Theoretical probability: Based on theoretical population distribution.
2. Classical probability: Based on theoretical possibilities and the ratio of favorable to possible events.
3. Empirical probability: Based on observations and the ratio of occurrences to observations.
How do you calculate classical probability for a single event?
Probability = Number of favorable events / Number of all possible events.
What is the probability of rolling a 6 on a six-sided die?
Probability = 1/6.
What is the probability of rolling a 6 or higher on a 20-sided die?
20 total events = 15/20 = 0.75.
How do you calculate the probability of independent events?
The probability of independent events occurring is the product of the individual probabilities. Example: p(5 tails in a row) = 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/32.
What is the Gambler’s Fallacy?
The belief that an outcome is more likely to occur because it hasn’t occurred in a while. For example, thinking “tails is due” after several heads in a row.
How do you calculate the probability of two independent events happening together?
Multiply their individual probabilities: p(A and B) = p(A) × p(B).
What is empirical probability?
Probability based on observed data. Formula: p = Number of times an event occurs / Number of observations.
How do you calculate empirical probability with a dataset?1
If 5 out of 15 participants drink 2 cups of coffee, the probability is p = 5/15 = 0.33.
What is theoretical probability?
Probability calculated based on theoretical population distributions, often using mathematical models.
