Key Terms
EXPERIMENT
A planned operation carried out under controlled conditions where the result is not predetermined. Rolling a die, flippi
OUTCOME
A single result of an experiment.
SAMPLE SPACE (S)
The complete set of all possible outcomes. Example: flip one coin — S = {H, T}
EVENT
Any combination of outcomes; represented by uppercase letters (A, B, C). P(A) means "the probability of event A."
PROBABILITY
The long-term relative frequency of an outcome. Always a number between 0 and 1, inclusive.
EQUALLY LIKELY
Each outcome has the same chance of occurring. Formula when outcomes are equally likely: P(A) = (number of outcomes in A
LAW OF LARGE NUMBERS
As the number of repetitions increases, the observed (empirical) relative frequency gets closer and closer to the theore
BIAS
A coin or die may not be fair. Unfair means outcomes are not equally likely.
OR EVENT
Outcome is in A OR B if it is in A, B, or both. No duplicates.
Example
S = {1 through 12}, A = {1,2,3,4,5,6}, B = {6,7,8,9} A AND B = {6} A OR B = {1,2,3,4,5,6,7,8,9} Neither A nor B = {10,11
AND EVENT
Outcome is in A AND B only if it is in both simultaneously. A AND B = {4,5}
Formula
P(A|B) = P(A AND B) / P(B), where P(B) > 0
DEFAULT RULE
If you don't know whether A and B are mutually exclusive, assume they are NOT until proven otherwise.
SAMPLING WITH REPLACEMENT
After each pick, the item goes back. The next pick is unaffected.
SAMPLING WITHOUT REPLACEMENT
Item is removed after each pick. The next pick is affected by what was already taken.