03 Probability Free Online FlashCards

What range can a probability have?

A probability is a number from 0 to 1, where 0 means impossible and 1 means certain; it may also be expressed as a percentage.

What is the difference between a sample space and an event?

The sample space is the set of all possible outcomes, while an event is a subset of that sample space.

How is an equally likely event probability calculated?

For equally likely outcomes, $P(A)=\frac{\text{number of outcomes in }A}{\text{number of outcomes in }S}$.

What is the complement rule?

The complement $A^c$ contains outcomes not in $A$, and its probability is $P(A^c)=1-P(A)$.

What do intersection and union mean?

The intersection $A\cap B$ means both events occur; the union $A\cup B$ means at least one occurs, including the possibility that both occur.

What is the general addition rule?

The general addition rule is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. The intersection is subtracted because it was counted twice.

What does the multiplication principle count?

If successive steps have $m$ choices and $n$ choices, the process has $m\times n$ possible outcomes; multiply across additional steps.

When should you use a permutation?

A permutation is an arrangement in which order matters. Selecting a president and vice president is a permutation because the roles differ.

What is the permutation formula?

The number of permutations of $r$ objects selected from $n$ distinct objects is ${}_nP_r=\frac{n!}{(n-r)!}$.

When should you use a combination?

A combination is a selection in which order does not matter. A three-person committee is a combination because membership, not ordering, matters.

How is conditional probability defined?

For $P(B)>0$, conditional probability is $P(A\mid B)=\frac{P(A\cap B)}{P(B)}$. The condition restricts attention to outcomes in $B$.

What does it mean for two events to be independent?

Events are independent when one occurring does not change the probability of the other; equivalently, $P(A\cap B)=P(A)P(B)$.