Transcript Chapter 6 - Probability

Chapter 6 - Probability
Math 22
Introductory Statistics
Simulating Repeated Coin Tosses
with the TI – 83
 Empirical Probability (Observed Probability) –
The probability of a specific event as it was
observed in an experiment.
 Theoretical Probability – The true probability of
a specific event of interest. Often an unknown
value estimated by an empirical probability.
 Simulation
Probability
 Probability
- A numerical value that is associated
with some outcome and indicates how likely it is
that the outcome will occur.
 Experiment - The process of making an
observation or taking a measurement.
 Sample Space (S) - Listing of all possible
outcome of an experiment.
 Event - Subset of the sample space.
Probability of an Event
The probability of an event A is the sum of the
outcomes in A. We write it as P(A).
P(event) = # of times that the event can occur
total # of outcomes in the experiment
Assigning Probabilities to Individual
Outcomes
In assigning probabilities to the individual
outcomes in a sample space, two conditions must
be satisfied:
 The probability of each outcome must be between
0 and 1, inclusive.
 The probabilities of all outcomes in the sample
space must sum to 1.
Calculating the Probability of an
Event
 Define
the experiment and list the outcomes in the
sample space.
 Assign probabilities to the outcomes such that each
is between 0 and 1.
 List the outcomes of the event of concern.
 Sum the probabilities of the outcomes that are in
the event of concern.
Law of Large Numbers
 As
the number of times an experiment is repeated
increases (as n gets larger), the value of the
empirical probability will approach the value of the
theoretical probability.
Odds and Compliment of an Event
 Odds
of an Event – The probability of that
event not happening.
 Compliment
General Addition Rule
 Let
A and B be events then,
P A  B  P( A)  P( B)  P( A  B)
Conditional Probability
 Conditional
Probability - The probability of an
event occurring given that another event has
already occurred.
The Multiplication Law for
Independent Events
 Let A and
B be two independent events then
P(A and B)=P(A)P(B)