PHIL 105 - Unit 6 Formulas

Basic Probability Calculation (For Equally Likely Outcomes, i.e. Coin Flip)

P(A) = A-Outcomes/Total Possible Outcomes

Independent Probability (Conditional)

P(A) = P(A|B)

Not Independent Probability (Conditional)

P(A) =/= P(A|B)

Disjunction (Mutually Exclusive) (Chance that either A or B happens)

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

Disjunction (Not Mutually Exclusive) (Chance that A or B happens, but A and B could potentially both happen in one)

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

Negation Rule

P(A) = 1 - P(Not-A) [Also: P(Not-A) = 1 - P(A)]

Conjunction Rule (Independent Events) (Chance of two coins landing heads)

P(Aheads-and-Bheads) = P(Aheads) x P(Bheads)

Conjunction Rule (Not Independent Events) (Chance of A and B both happening in one)

P(A-and-B) = P(A|B) x P(B) = P(B|A) x P(A)

Disjunction of Conjunctions (Movie Sleep Example - Overall chance of sleep given chance of sleep with specific genres + chance that those genres will be picked) (Comparing probabilities)

P(Abd) = (P(Abd|Xen) x P(Xen)) + (P(Abd|Zar) x P(Zar)) + (P(Abd|OP) x P(OP)). [P(Abd) = P(Xen-and-Abd) + P(Zar-and-Abd) + P(OP-and-Abd)]

Joint Probablility

Chance of 2 events: P(A-and-B)

Conditional Probability

Chance of one event (A): P(A|B)

Expected Value

Expected Value = (A-Value x P(A)) + (B-Value x P(B))

At Least One

P(AL1-A(N Cases)) = 1 - (1 - P(A))^N

Chance of All being A

P(A)^N (N = total (i.e. chance of 5 coins all being heads = P(Heads)^5)