● Sample Space: The collection of all possible outcomes of a chance experiment
● Event: Any collection of outcomes from the sample space
● Complement: Consists of all outcomes that are not in the event
● Union: The event A or B happening
○ Consists of all outcomes that are in at least one of the two events
○ E = A ∪ B
● Intersection: The events A and B happening
○ Consists of all outcomes that are in both events
○ E = A ∩ B
● Mutually Exclusive (Disjoint): Two events have no outcomes in common
● Venn Diagrams: Used to display relationships between events
○ Helpful in calculating probabilities
● Probability: Denoted by P (Event)
○ P(E) = Favorable Outcomes/Total Outcomes
■ Only appropriate when the outcomes of the sample space are equally likely
● Experimental Probability: The relative frequency at which a chance experiment occurs
● Law of Large Numbers: As the number of repetitions of a chance experiment increase, the difference between the relative frequency of occurrence for an event and the true probability approaches zero
● Independent: Two events are independent if knowing that one will occur does not change the probability that the other occurs
● Legitimate Values: For any event E, 0 ≤ P(E) ≤ 1
● Sample Space: If S is the sample space, P(S) = 1
● Complement: For any event E, P(E) + P(Not E) = 1
● Addition: Two events A and B, P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
● Multiplication: If two events A and B are independent, P(A ∩ B) =
P(A) • P(B)
○ General Rule: P(A ∩ B) = P(A) * P(B/A)
● At Least One: P(At Least 1) = 1 - P(None)
● Conditional Probability: Probability that takes into account a given condition
○ P(A/B) = P(A ∩ B)/P(B)
● nCr = n!/(n-r)! r!
● nCr = nCn - r
● Order does not matter with combinations
○ A, B, C
○ 3C1 = A, B, C
○ 3C2 = AB, BC, AC
● nCr prqn-r
○ n = Number of Trials
○ r = Number of Successes
○ p = P(Success)
○ q = P(Not Success) = 1 - p
● σ = √(∑(x - x̅)2/n)
● S = √(∑(x - x̅)2/(n - 1))
● E(X ± Y) = E(X) ± E(Y)
○ E(X) = x̅
○ E(Y) = ȳ
● σ2(X ± Y) = σ2(X) + σ2(Y)