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ALGEBRA 2 LECTURE P – 1:
Introduction to Probability
Reading Assignment: Chapter 10, Pages 628 – 642
PROBABILITY
Probability is the extent to which an event is likely to occur, measured by the ratio of the favorable
cases to the whole number of cases possible.
Probability is expressed as a number from 0 to 1, inclusive. It is often written as a fraction, decimal or
percent.
 An impossible event has a probability of 0
 An event that must occur has a probability of 1
 The sum of the probabilities of all outcomes in a sample space is 1
EXPERIMENTAL PROBABILITY
 Approximated by performing trials and recording the ratio of the number of occurrences of the
event to the number of trials
THEORETICAL PROBABILITY
 Based on the assumption that all outcomes in the sample space occur randomly.
Theoretical Probability Formula
P(E) = probability that an event, E, will occur.
n(E) = number of equally likely outcomes of E.
n(S) = number of equally likely outcomes of sample space S.
EXAMPLE 1: Find the probability of randomly selecting a red disk in one draw from a container that
contains 2 red disks, 4 blue disks, and 3 yellow disks.
TRY THIS PAGE 629: Find the probability of randomly selecting a blue disk in one draw from a
container that contains 2 red disks, 4 blue disks, and 3 yellow disks.
FUNDAMENTAL COUNTING PRINCIPLE
If there are m ways that one event can occur and n ways that another event can occur, then there are
m x n ways that both events can occur.
ALGEBRA 2 LECTURE P – 1:
Introduction to Probability
EXAMPLE 2: Ann is choosing a password for her access to the Internet. She decides not to use the
digit 0 or the letter O. Each letter or number may be used more than once. How many passwords of 2
letters followed by 4 digits are possible?
TRY THIS PAGE 632: A license plate consists of 2 letters followed by 3 digits. The letters, A – Z,
and the numbers, 0 – 9, can be repeated. Find the probability that your new license plate contains the
initials of your first and last names in their proper order.
PERMUTATIONS
PERMUTATION
An arrangement of objects in a specific order
The number of permutations of n objects is given by n!
n! = n factorial = n x (n – 1) x (n – 2) x ….. x 2 x 1
EXAMPLE 3: In 12-tone music, each of the 12 notes in an octave must be used exactly once before
any are repeated. A set of 12 tones is called a tone row. How many different tone rows are possible?
TRY THIS PAGE 637: How many different ways can the letters in the word objects be arranged?
PERMUTATIONS OF n OBJECTS TAKEN r AT A TIME
The number of permutations of n objects taken r at a time, denoted by P(n,r) or nPr, is given by
where r  n.
EXAMPLE 4: Find the number of ways to listen to 5 different CDs from a selection of 15 CDs.
TRY THIS PAGE 637: Find the number of ways to listen to 4 different CDs from a selection of 8
CDs.
HW P – 1 Page 633 #9 – 23 Odds, 27 & 29; Page 640 #25 – 43 Odd