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Today in Precalculus
• Go over homework
• Introduction to Probability
• Homework
Probability - Definitions
Probability – a ratio that represents the likelihood
of something occurring
Sample Space – the set of all possible outcomes
Event – a subset of the sample space
Probability of an Event
(equally likely outcomes)
If E is an event in a finite, non-empty sample space S
of equally like outcomes, then the probability of the
event E is: P( E )  the number of outcomes in E
the number of outcomes in S
Example: Find the probability of rolling an odd
number on a single roll of a fair die
1,3,5
1
P(odd ) 

1, 2,3, 4,5, 6 2
Probability
Let p be the probability of a given event
then the probability of outcome is: 0≤p≤1
The sum of all probabilities in S (event space) is
1.
A set with no elements is the empty set,Æ so
P(Æ)=0
Probability when outcomes
are not equally likely
Example: What is the probability of rolling a
sum of less than 6 when two die are rolled.
Sums of two die are between 2 and 12 but not
all are equally likely.
Must determine individual probabilities first.
Example (cont.)
Outcome Probability
2
1/36
3
2/36
4
3/36
5
4/36
6
5/36
7
6/36
8
5/36
9
4/36
10
3/36
11
2/36
12
1/36
P(sum less than 6)=
P(sum 2,3,4,or 5)=
1/36 + 2/36 + 3/36 + 4/36 =
10/36 =5/18
Multiplicity principle of
Probability
Suppose event A has probability p1 and event B has
probability p2 under the assumption that event A has
already occurred.
Then the probability that A and B occur is p1•p2
12
So P(two aces) = 4 3

52 51

2652
 .0045
The probability of NOT drawing 2 aces?
1 - .0045 = .9955
Probability
Keep in mind in math, the word OR signifies addition
while the word AND signifies multiplication.
Ex: Find the probability of drawing an ace or a king
from a deck of cards is 4
4
8
2
52

52

52

13
Ex: Find the probability of drawing an ace and a king
from a deck of cards is 4
4
16

52 51

2652
 0.006
Homework
• Pg 728:1-25 odd
• Quiz: Friday, January 29