Department

SpanishCourse Code

SPAN 101Professor

Enrique ManchonChapter

7This

**preview**shows page 1. to view the full**4 pages of the document.**CH 7 RANDOMNESS AND PROBABILITY

Law of large numbers: relative frequency of a random event settles down to a single

number in the long run

Different Types of probability

Model based (theoretical) probability:

o Empirical probability – the relative frequency of an event’s occurrence as the

probability of an event

o P(A) = # of outcomes in A / total # of outcomes

Personal Probability:

o Personal assessment of an event expresses your uncertainty about the

outcome

o Not based either on long run relative frequencies or equally likely events

o Satisfy the same rules as both empirical and theoretical probabilities

Probability Rules:

Rule 1: a probability is a number between 0 & 1.

0<= P(A) <=1

Rule 2: probability assignment rule: the probability of the set of all possible

outcomes must be 1

P(S) = 1 ; where s represents the set of all possible outcomes

Rule 3:the set of outcomes that are not in the event A is called complement of A, Ac

Complement Rule: the probability of an event occurring is 1 minus the probailtiy

that it doesn’t occur

P(A) = 1 – P(AC)

Rule 4: multiplication rule: for 2 independent events A and B, the probability that

both A and B occur is the product of the probabilities of the 2 events

P(A and B) = P(A) x P(B), A and B are independent

Rule 5: addition Rule: add the probabilities of disjoint events to get the probability

that either event occurs:

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

Rule 6: General Addition Rule: add the probabilities of two events and then subtract

the probability of their intersection

P(A or B) = P(A) + P(B) – P (A and B)

Marginal probability: only totals found in the margins of the table

Joint probability: probability of two events occurring together

Conditional probability: takes into account a given condition

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

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