Transcript AP Statistics

AP Statistics
Notes Chapter 14 and 15
Notes Chapter 14

Probability is the branch of mathematics that
describes the pattern of chance outcomes.
 Random is a description of a kind of order that
emerges only in the long run. Individual
outcomes are uncertain but there is a regular
distribution of outcomes in a large number of
repetitions.
 The probability of any outcome is the
proportion of times the outcome would occur in
a very long series of repetitions.

For any random phenomenon, each attempt, or trial,
generates an outcome.
 The sample space, S, of a random phenomenon is
the set of all possible outcomes for a variable. (Be
sure you know what variable you are representing.)
 Sampling can be done with or without replacement.
Determining which to use is generally done from the
context of the problem.
 An event is an outcome or a set of outcomes of a
random phenomenon, a subset of the sample space.

Disjoint events, also called mutually
exclusive, have no outcomes in common.
They can not occur at the same time.
 Events are independent (informally) when the
outcome of one event does not influence the
outcome of any other event.
 Be certain not to confuse disjoint with
independent. Disjoint events cannot occur
together, therefore they cannot be
independent.

The Law of Large Numbers says that the
long-run relative frequency of repeated
independent events settles down to the true
probability as the number of trials increases.
 A probability distribution for a certain
variable is made up of the sample space, S,
and the individual probabilities of each event in
the sample space.
 The following three rules apply to probability
distributions. S represents the sample space
and x any event in the sample space.

Rule 1: The probability of any event is a number
between 0 and 1. 0  P(x)  1.

Rule 2: The sum of all possible outcomes must
equal 1. P(S) = 1.
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Rule 3: The probability that an event does not
occur is 1 minus the probability that the event does
occur.
This is called the probability of the complement, Ac.
P(Ac) = 1 – P(A)
An urn has 10 marbles in it. 4 are
red, 3 are blue, 2 are green and 1
is purple.
Chapter 15
The union (U) of any collection of events
is the event that at least one of the
collection occurs. Union of two events is
when either one or the other, or both
events occur.
 The intersection (∩) of any collect of
events is when all the events occur.
Intersection of two events is when both
event A and event B occur.

Venn Diagrams:
Conditional Probability: P(B|A)
 This is read as “the probability of B given
A. It is the conditional probability that
event B occurs given that event A
occurs.


There are two rules of probability that are
given on the AP Statistics formula sheet. The
first is:
 General Addition Rule for Union of Two
Events
For any two events A and B,
P(A U B) = P(A) + P(B) – P(A ∩ B)
 The second stems from the general
multiplication rule which states:

General Multiplication Rule
P(A ∩ B) = P(B)P(A|B)
 Based on the last formula we can define a rule
for conditional probability:
 OR….
When P(A) > 0,
P(A|B) = P(A ∩ B)
P(B)
 This is the second formula for probability on
the AP Stat formula chart.
Independent Events – formally
Two events A and B that both have positive
probability are independent if
P(B|A) = P(B)
 In other words, the probability of event B is not
affected by the event A. This fits with the
informal definition of independence but now
gives us a way to show two events are
independent mathematically. This formula is
not on the AP Stat formula chart.

Making Tree Diagrams…
Making Tables….
Example1: page 341 #24
The American Red Cross says that
about 45% of the U.S. Population has
Type O blood, 40% Type A, 11% Type
B, and rest Type AB.
 A) Someone volunteers to give blood.
What is the probability that this donor

1. has Type AB blood?
 2. has Type A or Type B?
 3. is not Type O?
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Example 1 continued

The American Red Cross says that about 45%
of the U.S. Population has Type O blood, 40%
Type A, 11% Type B, and rest Type AB.
 B) Among four potential donors, what is the
probability that
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


1. All are Type O?
2. no one is Type AB?
3. they are not all Type A?
4. at least one person is Type B?
Example 2: Birthday Gifts

In a book titles, Birthday Gifts, Brier and
Rogers found that 71% of married men
will get flowers or buy jewelry for their
wives on their birthdays. 58% of married
men will buy jewelry and 39% will buy
flowers for their wives. What is the
probability that a married man will buy
flowers and jewelry for his wife’s
birthday?
Example 3: Oh, Say can you see?
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In the book Chances: Risk and Odds in Everyday Life,
James Burke says that 56% of the general population
wears eyeglasses, while only 3.6% wears contacts. He
also says that of those who wear glasses, 55.4% are
women. Of those who wear contacts, 36.9% are men.
Assume that no one wears both glasses and contacts.
For the next person you encounter at random, what is
the probability that this person is:
A) not wearing contacts
B) a woman wearing glasses
C) a man wearing contacts
Example 4: Brown Hair/ Brown Eyes

In a certain town, 40% of the people have brown hair,
25% have brown eyes, and 15% have both brown hair
and brown eyes. A person is selected at random from
the town.

1. If he or she has brown hair, what is the probability
that he or she also has brown eyes?
2. If he or she has brown eyes, what is the probability
that he of she does not have brown hair?
3. What is the probability that he or she has neither
brown hair or brown eyes?
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Example 5: What does your GPA say?
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This example does not fit on one slide,
so we will have to use the document
camera!!!