Probability
Chapter 12
Sample Spaces and
Probability
I can find theoretical and experimental
probabilities.
Sample Spaces and
Probability
Vocabulary (page 357 in Student Journal)
probability experiment: an action (trial) that
has varying results
outcome: the results of a probability
experiment
event: a collection of 1 or more outcomes
Sample Spaces and
Probability
sample space: the set of all the possible
outcomes
probability of an event: the measure of the
likelihood an event will occur
theoretical probability: a probability based
on what is expected to happed
Sample Spaces and
Probability
geometric probability: a probability based
on the ratio of 2 lengths, areas, or volumes
experimental probability: a probability
based on the results of repeated trials in a
probability experiment
Sample Spaces and
Probability
Core Concepts (page 357 in Student
Journal)
Probability of the Complement of an Event
P(A’) = 1 – P(A), where P(A) is the probability
of event A and P(A’) is the probability of the
complement of event A
Sample Spaces and
Probability
Examples (page 357 in Student Journal)
A coin is flipped 4 times.
a) What is the probability it lands on tails exactly
3 times?
b) What is the probability it lands on tails less
than 3 times?
c) What is the probability it lands on tails 3 or
more times?
Sample Spaces and
Probability
Solutions
a) 1/4
b) 11/16
c) 5/16
Sample Spaces and
Probability
d) What is the probability you throw a dart
and it lands in one of the 2 yellow sectors in
the small circle?
Sample Spaces and
Probability
Solution
d) 0.063
Sample Spaces and
Probability
e) A spinner has 5 equal sized sections of
various colors. The results after 50 spins are
shown in the table. How does the
theoretical probability of the spinner
landing on yellow compare to its
experimental probability?
Sample Spaces and
Probability
Solution
e) the probabilities are the same (1/5)
Independent and Dependent
Events
I can find probabilities of independent and
dependent events and find conditional
probabilities.
Independent and Dependent
Events
Vocabulary (page 362 in Student Journal)
independent events: the occurrence of 1
event does not effect the occurrence of
another event
dependent events: the occurrence of 1
event does effect the occurrence of
another event
Independent and Dependent
Events
conditional probability: the probability of an
event occurring, given that another event
has already occurred
Independent and Dependent
Events
Core Concepts (pages 362 and 363 in
Student Journal)
Probability of Independent Events
Two events are independent if and only if
the probability that both events occur is the
product of the probabilities of the events.
Independent and Dependent
Events
Probability of Dependent Events
If 2 events are dependent events, the
probability that both events will occur is the
product of the probability of the first event
and the conditional probability of the
second event.
Independent and Dependent
Events
Examples (space on pages 362 and 363 in
Student Journal)
A bag contains 10 red marbles and 5 blue
marbles.
a) What is the probability of selecting 3 blue
marbles if you replace the marbles after
drawing them?
b) What is the probability of selecting 3 blue
marbles if you do not replace the marbles after
drawing them?
Independent and Dependent
Events
Solutions
a) 1/27
b) 2/91
Independent and Dependent
Events
A quality control inspector checks for defective
parts. The table shows his findings after 1 week.
c) Find the probability a defective part passes.
d) Find the probability that a non-defective part
passes.
Independent and Dependent
Events
Solutions
c) 5/29
d) 208/217
Independent and Dependent
Events
e) At a clothing store, 75% of customers buy
pants. Only 20% of customers buy pants
and a belt. What percent of customer who
buy pants also buy a belt?
Independent and Dependent
Events
Solution
e) 4/15
Two-Way Tables and
Probability
I can make two-way tables.
Two-Way Tables and
Probability
Vocabulary (page 367 in Student Journal)
two-way table: a frequency table that
displays data collected from 1 source that
belongs to 2 different categories
joint frequency: each entry in a two-way
table
Two-Way Tables and
Probability
marginal frequency: the sums of the rows and
columns in a two-way table
joint relative frequency: the ratio of the joint
frequency to the total number of observations
marginal relative frequency: the ratio of the
marginal frequency to the total number of
observations
Two-Way Tables and
Probability
conditional relative frequency: the ratio of a
joint relative frequency to a marginal
relative frequency
Two-Way Tables and
Probability
Examples (space on page 367 in Student
Journal)
A store surveys customers of different ages
to see if they would like to see the toy
department expanded. The results are in
the two-way table.
Two-Way Tables and
Probability
a) What is the probability a randomly selected
person whose age is between 10 and 20 said no?
b) What is the probability a randomly selected
person who said yes is younger than 10?
c) Are the events replying yes and being younger
than 10 independent?
Two-Way Tables and
Probability
Solutions
a) 73.9%
b) 48.2%
c) no
Probability of Disjoint and
Overlapping Events
I can find probabilities of compound
events.
Probability of Disjoint and
Overlapping Events
Vocabulary (page 372 in Student Journal)
compound event: the union or intersection
of 2 events
overlapping events: 2 events that have 1 or
more outcome in common
Probability of Disjoint and
Overlapping Events
disjoint (mutually exclusive) events: 2
events that have no outcomes in common
Probability of Disjoint and
Overlapping Events
Core Concepts (page 372 in Student
Journal)
Probability of Compound Events
P(A or B) = P(A) + P(B) – P(A and B)
If the events are disjoint, then P(A or B) =
P(A) + P(B).
Probability of Disjoint and
Overlapping Events
Examples (space on page 372 in Student
Journal)
A 6-sided die is rolled.
a) What’s the probability of rolling a 3 or a
4?
b) What’s the probability of rolling a 2 or an
even?
Probability of Disjoint and
Overlapping Events
Solutions
a) 1/3
b) 1/2
Probability of Disjoint and
Overlapping Events
c) A medical association estimates 10.9% of
people in the US have a thyroid disorder. A
lab has a simple diagnostic test that is 96%
accurate for people who have the disorder
and 99% accurate for people who do not.
What’s the probability the diagnosis is
correct for a randomly selected person?
Probability of Disjoint and
Overlapping Events
Solution
c) 98.7%
Permutations and
Combinations
I can use the formula for permutations and
the formula for combinations.
Permutations and
Combinations
Vocabulary (page 377 in Student Journal)
permutation: an arrangement of objects in
which order is important
n factorial: the product of integers from 1 to n
combination: a selection of objects in which
order is not important
Permutations and
Combinations
Examples (space on pages 377 and 378 in
Student Journal)
a) In how many ways can you arrange the
letters in the word PENCILS?
b) 8 people are in a race. How many ways
can they finish 1st, 2nd or 3rd?
Permutations and
Combinations
Solutions
a) 5040
b) 336
Permutations and
Combinations
c) You are listening to music and only have
time to listen to 3 songs. How many
combinations of 3 songs are possible if you
have 16 songs on your playlist?
Permutations and
Combinations
Solution
c) 560