MATH 273 Chapter Notes - Chapter 12-13: Mutual Exclusivity, Empirical Probability
30 May 2018
School
Department
Course
Professor
Chapter 12
Theoretical probability: straight forward, if you roll a die once, what is the probability that you
will get 1 = P (1) = 1/6. Sometimes called mathematical or classical. P(A) = number of times A
occurs/ total number of trials
Empirical probability: calculate with histograms and everything. More complex. P(A) = # of
outcomes in A/ # of equally likely possible outcomes.
The law of large numbers: the long-run relative frequency of repeated independent events gets
closer and closer to a single value. Says nothing about short-term behavior.
Rules of probability:
Rule 1: probability can only be between 0 and 1. And the probability percentage cannot be
egatie. % does’t ake sese either. Proailities are ritte i deials .45 is 45%
Rule 2: the set of all possible outcomes should be 1 (100%). One means it always occurs. Zero
probability means it cannot occur.
Rule 3 (Complement Rule): The probability of an event occurring is 1 minus the probability that
it does’t our:
P(A) = 1 – P(AC)
Complement rule Example: Ex. 1: At the traffic light on the corner of York Road and Bosley Avenue the
northbound light is green about 35% of the time.
What is the probability that the light is not green when you get to the intersection?
P (not green) = = 1 - .35 = 0.65
Copleetary eets ea that the outoe of oe eet does’t affet the outoe of the
other event.
Disjoint means that the probability of two events occurring at the same time is zero.
*All complementary events are disjoint, but all mutually exclusive events are not necessarily
complementary. *
Additio rule uses or or uio sig U. “peial ases for disjoit eets.
Multipliatio rule uses ad or ∩. Special independent events.
Formula:
P (A or B) = P(A) + P(B) – P (A and B)
Special addition rule for disjoint events:
find more resources at oneclass.com
find more resources at oneclass.com
