Probability. Rules  0 ≤ P(A) ≤ 1 for any event A.  P(S) = 1  Complement: P(A c ) = 1 – P(A)  Addition: If A and B are disjoint events, P(A or B) =

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Presentation transcript:

Probability

Rules  0 ≤ P(A) ≤ 1 for any event A.  P(S) = 1  Complement: P(A c ) = 1 – P(A)  Addition: If A and B are disjoint events, P(A or B) = P(A) + P(B).  Multiplication: If A and B are independent events, P(A and B) = P(A)P(B).

Reminder  Disjoint – mutually exclusive (no outcomes in common, never occur simultaneously, one happens then the other.  Independent – knowing one outcome doesn’t change the other outcome.

Joint Probability  JOINT – (opposite of disjoint) mutually inclusive (some common outcomes, can occur simultaneously). The union is less than the sum of the individual probabilities. P(A or B) = P(A) + P(B) – P(A and B). P(A or B) = P(A) + P(B) – P(A and B).

Exercises  6.27, 6.30, 6.31, 6.33, , 6.46, 6.47, 6.52, 6.53

Conditional Probability  Probability changes if we know that some other event has occurred.  New Notation: P(A|B) read “Probability of A given the information about the probability of B”

Multiplication Rule  The probability that both of two events A and B happens together P(A and B) = P(A)P(B|A) P(A and B) = P(A)P(B|A) Conditional is P(B|A) which is to say that B occurs given that A occurs.

Conditional Probability  When P(A) > 0, the conditional probability of B given A is  P(B|A) = P(A and B)/ P(A)  Homework: 6.54 – 6.56

Extended Multiplication Rules  Intersection – the event that all of the events occur.  P(A and B and C) = P(A)P(B|A)P(C|A and B)