Introduction to Probability Flashcards
In a random event, outcomes are
uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions
the probability of any outcome of a random phenomenon
the proportion of times the outcome would occur in a very long series of repetitions.
Probability models mathematically describe the outcome of random processes. They consist of two parts:
1) S = Sample Space: This is a list or description, of all possible outcomes of a random process.
An event is a subset of the sample space.
2) A probability assigned for each possible simple event in the sample space S.
Discrete vs Continuous sample space
Discrete sample space: Discrete variables that can take on only certain values (a whole number or a descriptor).
Continuous sample space: Continuous variables that can take on any one of an infinite number of possible values over an interval.
Probabilities rage from
Probabilities of a sample space
Two events are disjoint, or mutually exclusive, if they
can never happen together (have no outcome in common).
Addition rule for disjoint events vs General addition rule for any two events A and B
Continuous sample spaces contain
an infinite number of events.
use ______ to model continuous probability distributions.
density curves
They assign probabilities over the range of values making up the sample space.
The total area under a density curve represents ____
Probability are computed as ___
The probability of an event being equal to a single numerical value is zero when ____
the whole population (sample space) and equals 1 (100%).
areas under the corresponding portion of the density curve for the chosen interval.
the sample space is continuous (infinite number of events)
Risk
The risk of an undesirable outcome of a random phenomenon is the probability of that undesirable outcome.
risk(event A) = P(event A)
The odds of any outcome
of a random phenomenon is the ratio of the probability of that outcome occurring over the probability of that outcome not occurring.
odds(event A) = P(event A) / [1 − P(event A)]
