1 Probability Foundations and Sample Spaces Free Online FlashCards

What is a sample space?

A sample space is the set of all possible outcomes of a probability experiment, denoted by $S$.

What is an outcome?

An outcome is the result produced by one trial of a probability experiment.

What is an event in probability?

An event is a subset of the sample space representing outcomes of interest.

What does the complement $A^c$ represent?

The complement $A^c$ contains every outcome in $S$ that is not in $A$.

What does $A\cup B$ mean?

The union $A\cup B$ contains outcomes in $A$, in $B$, or in both; it represents “$A$ or $B$.”

What does $A\cap B$ mean?

The intersection $A\cap B$ contains outcomes common to both events; it represents “$A$ and $B$.”

What range must every probability satisfy?

For any event $A$, probability satisfies $0\le P(A)\le 1$.

How is probability found for equally likely outcomes?

If all outcomes are equally likely, $P(A)=\frac{|A|}{|S|}$: favorable outcomes divided by total outcomes.

What is the complement rule?

The complement rule is $P(A^c)=1-P(A)$.

What is the general addition rule?

The addition rule is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$.

What is conditional probability?

When $P(A)>0$, conditional probability is $P(B\mid A)=\frac{P(A\cap B)}{P(A)}$.

What is the multiplication rule?

The multiplication rule is $P(A\cap B)=P(A)P(B\mid A)$.