Statistics CH5 - Probability in our daily lives.

Probability

A way to quantify uncertainty; measures the chance of possible outcomes for random phenomena

Random phenomena

Any observable occurrence with unpredictable specific outcomes

Randomness

The unpredictable variation in outcomes when conducting experiments or collecting data

Trial

One repetition or observation in an experiment

Cumulative proportion

The running total proportion of successes observed across multiple trials

Law of large numbers

A principle stating that as more trials are conducted, the cumulative proportion approaches the true probability

Independent trials

Trials where the outcome of any one trial does not affect the outcome of any other trial

Subjective probability

A probability estimate based on personal judgment or experience rather than long-run data

Objective probability

A probability estimate based on mathematical calculations or long-run data

Sample space

The set of all possible outcomes of a random phenomenon

Tree diagram

A branching diagram representing all possible outcomes in a sequence of events

Event

A subset of the sample space; a particular outcome or group of outcomes

Probability model

A mathematical description specifying possible outcomes and assumptions for probability calculations

Independent events

Two events where the occurrence of one does not affect the probability of the other

Disjoint events

Also called mutually exclusive events; events with no outcomes in common

Complement

The set of outcomes not in a specified event (e.g., Ac is the complement of event A)

Intersection

The set of outcomes in which two events both occur

Union

The set of outcomes in which at least one of two events occurs

Conditional probability

The probability of an event given that another event has occurred

Conditional proportions

Proportions derived from a subset (conditional) of the sample space

Addition rule

A rule for finding the probability that either of two events occurs

Multiplication rule

A rule for finding the probability that both of two events occur, especially for independent events

Sensitivity

The probability that a test detects a condition by giving a positive result when the condition is present

Specificity

The probability that a test detects absence of a condition by giving a negative result when the condition is not present

Bayes’s rule

A formula for finding reverse conditional probabilities

Statistical inference

The process of making population-level conclusions from sample data based on probability

Simulation

The use of repeated random sampling or modeling to estimate probabilities