Transcript Probability - Dripping Springs Independent School District

Probability
The Study of Randomness
The language of probability
Random is a description of a kind of
order that emerges only in the long run
even though individual outcomes are
uncertain.
The probability of any outcome of a
random phenomenon is the proportion
of times the outcome would occur in a
very long series of repetitions.
POP QUIZ!!!
Mongolian History 1300 – 1417
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2.
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5.
False
False
True
False
True
Mongolian Probability
The sample space of a random event is the
set of all possible outcomes.
What is the sample space for answering one
true/false question?
S = {T, F}
What is the sample space for answering two
true/false questions?
S = {TT, TF, FT, FF}
What is the sample space for three?
Tree diagram
True
True
False
True
True
False
False
True
True
False
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True
False
False
S = {TTT, TTF, TFT, FTT, FFT, FTF, TFF,
FFF}
Multiplication Principle
Explain what you think the multiplication
principle is regarding our previous
example.
If you can do one task in a number of
ways and a second task in b number of
ways, both tasks can be done in a xb
number of ways.
If we had 5 true/false and 2 multiple
choice (5) on the quiz, how many
possible outcomes are possible?
Venn diagram: complement
S
A
Ac
General Addition Rule for
Unions of Two Events
For any two events A and B,
P(A or B) = P(A) + P(B) – P(A and B)
The union of any collections of event
that at least one of the collection occurs.
Venn diagram: union
S
A
B
Venn diagram: disjoint events
S
A
B
Examples
Suppose that 60% of all customers of a large insurance
agency have automobile policies with the agency, 40%
have homeowner’s policies, and 25% have both types of
policies. If a customer is randomly selected, what is the
probability that he or she has at least one of these two
types of policies with the agency?
P(A or B) = P(A) + P(B) – P(A and B)
P(auto or home) = .60 + .40 - .25 = .75
General Multiplication Rule
The joint probability that two events A
and B happen together can be found by
P(A and B) = P(A) P(B|A)
P(B|A) is the conditional probability that
B occurs given the information that A
occurs.
Multiplication Rule Practice
Drawing two aces with replacement.
 4  4 
P(2 aces)=      .0059
 52   52 
Drawing three face cards with replacement.
 12   12   12 
P(3 face)=        .0123
 52   52   52 
Multiplication Rule Practice
Draw 5 reds cards without replacement.
 26   25   24   23   22 
P(5 red)=            .0253
 52   51   50   49   48 
Draw two even numbered cards without
replacement.
 20   19 
P(2 even)=      .1433
 52   51 
Multiplication Rule Practice
Draw three odd numbered red cards
with replacement.
3
16 

P(3 odd)=    .0291
 52 
3
 8 
P(3 red, odd)=    .0036
 52 