Notes: The Counting Principle
The counting principle helps you find the total number of possible outcomes for a particular
The total number of ways a multipart event can happen is the PRODUCT of the
number of ways that the individual parts can happ
Properties of Powers
Products of Powers
Product of Powers Postulate:
A multiple choice test is two pages long. Each question has c possible choices. Page 1 has 5
questions. Page 2 has 8 questions. How many different ways can students answer if
Notes: Probability of Simple Events
Probability of an event is the ratio of the number of favorable outcomes to the total number of possible
outcomes. It is usually expressed as a fraction, decimal, or percent. It is always between 0 and 1 (0 P 1)
Notes: Probability of Compound Events
Compound events consist of 2 or more events.
If the outcome of one event does not affect the outcome of the other, the events are independent.
Independent events A and B:
P(A and B) = P(A) x P(B)
If the outcome of one
Positive and Negative Rational Exponents
In previous section learned that means the nth root of x.
In these sections will learn what happens when the numerator of the fraction is not a 1.
In other words, what does mean? See the Rational Exponent Theorem
Notes: Section 7.6, nth Roots
What is an nth Root?
We know that 5 is the square root of 25 because 52 = 25.
We know that 4 is the cube root of 64 because 43 = 64.
Square roots and cube roots are special cases of a more general idea: the nth root (n 1).
Notes: Section 7.3, Negative Integer Exponents
The Negative Exponent Theorem
Basically, if a base is being raised to a negative exponent, send it down to the denominator.
Note: bn and b-n are reciprocals of each other. (Recall that reciprocals a
Notes: Methods of Counting
Counting Method #1: Tree Diagrams
A restaurant offers a soup and sandwich lunch. There are 2 possible soups (tomato and chicken noodle); 3 types of bread
for the sandwich (white, rye, and wheat), and 4 meats (roast beef, ham, tu
We have already learned about sequences in this course. Today we are going to learn about a
new type of sequence. We also learned that sequences can have a recursive formula and an
Recall a Type of Sequence We Already
General Compound Interest Formula
A = Amount in the account
P = Principal amount (original amount you deposited)
r = Interest rate (always express it as a decimal and not a whole number, i.e. 5% would be 0.05)
n = Number of times per yea