Chapter 6 Flashcards
Sample space
the collection of all possible outcomes for an experiment or trial
Outcome
a single observation of an experiment
Event
an outcome or a set of outcomes for the experiment, that is, any subset of the sample space
Probability Model
a mathematical description of a random phenomenon consisting of two parts: a sample space and a way of assigning probabilities to events.
Property 1
The probability of an event is always between 0 and 1, inclusive (or between 0% and 100%, inclusive)
Property 2
The sum of the probabilities of all possible outcomes or trials must be 1.
[Sample space has a probability of 1]
Property 3
The probability of an event that cannot occur is 0 (impossible event). * E.g., it is impossible to throw two dice and the sum of them is 1.
Property 4
The probability of an event that is certain to occur is 1 (certain event). * E.g., if you throw two dice, the sum is 12 or less
Equal likelihood model
prediction based on some theoretical principle e.g., if you
toss a coin one time, chances of getting a head = 0.5
Law of Large Numbers (LLN)
The percentage or proportion of a large number of repetitions of the experiment tends towards a single value, which is the same as the equal-likelihood chance. e.g., if you toss a coin 1000 time, the percentage or proportion of the tosses that will be heads will be 0.5 or 50%
Mutually exclusive events (disjoint events)
two or more events, such that none of them have common outcomes (no overlap)
Events that are not mutually exclusive
have common outcomes overlap
Contingency Tables
Deal with bivariate, qualitative data
Show frequencies of two variables at the same time.
Marginal Probabilities
the probabilities of each category occurring for each variable
Joint Probabilities
the probabilities of joint events
= the probabilities of combinations of categories of the two variables
* Derived from the cells inside the contingency tables, which show joint events
Conditional Probability
the probability that event B occurs given that event A occurs
* Denoted P(B|A) – read “the probability of B given A”
If two events are Disjoint (Mutually exclusive)
Cannot be Independent
* In other words, they are dependent, one event will affect the other
If two events are Independent
Cannot be Disjoint
If two events are Joint
May or may not be Independent
If two events are Dependant
May or may not be Disjoint
Dependence ≠ Causality
Example * If someone gets a high mark in Chemistry, the probability that they get a high mark in Biology is also quite high.
