Honors Pre-Calculus
Name________________________________
Chapter 12 - Review
Date_______________Period__________
Learning Targets: Students will be able to analyze and interpret sets and apply counting theorems.
For problems 1-4, let
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}
M = {2, 5, 6, 8}
N = {1, 2, 3, 6, 8, 9, 11, 13} and P = {3, 4, 5, 6, 9, 12}.
Find the elements in the set.
1.
M   N  P
2.
M   N  P
3.
M N
4.
M N
Use the counting formula to solve the problem.
5.
6.
If n  A  15, n  A  B   43, and n  A  B   11, find n  B  .
Set R has 6 elements and set Q has 13
elements. If the two sets share 4 elements,
how many elements are there altogether?
7.
Set M has 19 elements and shares 3 elements
with set N. If there are 30 elements altogether,
how many elements are in only set N?
Solve the problem.
8.
In a class of 30 Pre-Calculus students, 18 are taking AP Physics, 15 are taking Rhetoric, 14 are taking AP US
History, 11 are taking Physics and Rhetoric, 9 are taking Rhetoric and History, 10 are taking History and Physics,
and 7 are taking all three.
a) Draw a Venn Diagram to represent the given data.
b) How many students are not taking AP Physics?
c) How many students are taking Rhetoric and Physics, but not History?
d) How many students are not in any of these classes?
Learning Targets: Students will be able to differentiate and use permutations, combinations, and the multiplication
principle of counting.
Solve the problem.
9.
Lisa has 5 skirts, 8 blouses and 2 jackets.
How many 3-piece outfits can she put
together assuming any piece goes with any other?
11.
A civic light opera production of Carousel is
holding auditions for the roles of Billy Bigelow,
Jigger Craigin, and Enoch Snow. If 35 men try
out for these roles, how many ways are there to
cast the roles?
10.
A certain mathematics test consists of 20
questions. Sarah decides to answer the
questions without reading them. In how many
ways can Sarah fill in the answer sheet if the
possible answers are true and false?
12.
How may 5-digit EVEN addresses can be
formed using the digits, 1, 2, 4, 5, and 7 if
a) repeated digits are allowed?
b) repeated digits are NOT allowed?
13.
On a shopping trip, you try on 8 sweaters, 7
pairs of pants and 5 pairs of shoes. Your mom
says that you’re only allowed to choose 3
sweaters, 4 pairs of pants, and 2 pairs of shoes.
How many different combinations are possible with
what you’re allowed to buy?
14.
How many different 11-letter words (real or
imaginary) can be made out of MISSISSIPPI?
15.
How many different 9-letter words (real or
imaginary) can be made out of TENNESSEE?
16.
How many 9-digit Social Security numbers
are possible if the first three digits are known
to be “330”?
17.
A bag contains 7 blue marbles, 11 yellow
marbles, and 6 white marbles. If 5 marbles are
drawn, how many ways are there to draw:
18.
A bag contains 8 red marbles, 7 white
marbles, and 6 blue marbles. Find the
probability of obtaining a white marble in a
single draw.
a) 3 blue marbles and 2 yellow marbles?
b) at least 4 white marbles?
Learning Targets: Students will be able to compute probability with equally likely outcomes.
Solve the problems.
19.
A lottery game has balls numbered 1 through
17. What is the probability of selecting an
even numbered ball or a 13?
20.
A spinner has regions numbered 1 through 21.
What is the probability that the spinner
will stop on an even number or a multiple of 3?
21.
If you draw one card from a standard deck of
52 cards, what is the probability that the card
is either a club or a nine?
22.
A bag contains 5 red marbles, 4 blue marbles,
and 1 green marble. What is the probability
of choosing a marble that is not blue when one
marble is drawn from the bag?
Learning Targets: Students will be able to compute compound and Binomial Probabilities.
23.
A fair die is rolled 15 times. Find the
probability that exactly 11 fours are rolled.
24.
A spinner is divided into 5 equals sections
labeled 1, 2, 3, 4, and 5. What is the probability
you will land on 4 exactly 7 times in 12 spins?
25.
A traffic engineer is counting the number of
vehicles by type that turn into a residential
area. The table below shows the results of
the counts during a four-hour period. What is
the probability that the next vehicle passing
is an SUV or a dump truck?
26.
What is the probability that in a group of 15
people at least 2 people have the same birthday?
Assume that there are 365 day in a year.
27.
In a shipment of 50 calculators, 5 are known to
be defective. If 6 calculators are picked at
random, what is the probability that 2 are
defective?
Type of
Vehicle
Car
SUV
Van
Small Truck
Large Truck
Dump Truck
Other
Number
273
439
77
288
211
23
67