Stat Quiz Probability (intro)

Relative Frequency Probability

The proportion of times the outcome would occur if we observed the random process an infinite number of times.

Relative Frequency

The proportion of times the event occurs out of
the number of trials.

Disjoint or Mutually Exclusive

The relationship of two outcomes that cannot both happen in the same trial, i.e. P(A and B) = 0.

Addition Rule for disjoint events

If outcomes are disjoint, the probability that one or the other occurs is found by adding their individual probabilities.

General Addition Rule

P(A or B) = P(A) + P(B) - P(A and B)

∩

Symbol for intersection / "and"

U

Symbol for union / "or" (inclusive)

Sample Space (S)

The set of all possible outcomes. The total probability of a sample space must equal 1.

Complement

An event A together with its complement comprise the entire sample space.

Independent events

The outcome of one does not change the likelihood of the outcome of the other, i.e. P(A | B) = P(A).

Multiplication Rule for independent events

The probability of 2 *independent* events can be calculated as the product of their unconditional probabilities.

Conditional Probability

The probability of an event is computed under another condition (a known outcome or event). The outcome of interest A given condition B is
computed as:
P(A|B) =P(A and B)/P(B)

Joint Probability

A probability that measures the likelihood two or more events will happen concurrently.

Joint/And Probabilities from a tree diagram

When there are two events, this is found as P(A) x P(B | A)

General Multiplication Rule

P(A and B) = P(A) * P(B|A) = P(A|B) * P (B)

Independent Events Check

If one of the following holds true:
P(A|B)=P(A) ,
P(A and B)=P(A)*P(B),
then A and B are independent

Mutually Exclusive (Disjoint) Check

If one of the following holds true:
P(A and B) = 0,
P(A or B) = P(A) + P(B),
then A and B are mutually exclusive (disjoint)

mutually exclusive/disjoint

two or more events that cannot happen simultaneously

P(at least 1)

Solve via complements; P(at least 1) = 1 - P(none)

Two events cant be both independent and mutually exclusive.

Mutually exclusive means if one happens the other cannot – that is an extreme type of dependence. Knowing one happened changes the probability of the other to 0.

Coin flips, dice rolls

independent (no impact from event A to event B)

Drawing cards or colored marbles (w/o replacement)

dependent (the value changes from event A to event B)