Data is presented on hamburger purchases at a stand, with

2. An area of mathematics PROBABILITY
THEORY, provides a measure of the likelihood
of the outcome of phenomena and events.
Insurance companies use it to decide on financial
policies, the government uses it to determine its
fiscal and economic policies, theoretical physicists
use it to understand the nature of atomic – sized
systems in quantum mechanics, and public –
opinion polls.

3. Problem:
 A spinner has 4 equal sectors colored yellow,
blue, green and red. What are the chances of
landing on blue after spinning the spinner? What
are the chances of landing on red?

4. Solution:
 The chances of landing on blue are 1 in 4, or one
fourth.
 The chances of landing on red are 1 in 4, or one
fourth.

5. DEFINITION
 Probability is the measure of how likely an event
is.
 The probability of landing on blue is one fourth.

6.  An experiment is a situation involving chance or
probability that leads to results called outcomes.
 Example, the experiment is spinning the spinner.

7.  An outcome is the result of a single trial of an
experiment.
 Example, the possible outcomes are landing on
yellow, blue, green or red.

8.  An event is one or more outcomes of an
experiment. It is the subset of the sample space
Solution:
 One event of this experiment is landing on blue.

9.  Sample point space is the set of all possible outcomes
of an experiment. Each element of the sample space
is called sample point or simple outcome.
 Example:
1. If the experiment is tossing a coin, the
sample space is {heads, tails}.
2. If the experiment is drawing a card from a
bridge deck, one sample space is the set
of cards.
3. If the experiment is tossing a coin twice, a
sample space is {HH, HT, TH, TT}

10. Probability Of An Event
P(A) = The Number Of Ways Event A Can Occur
The total number Of Possible Outcomes

11.  The probability of event A is the number
of ways event A can occur divided by the
total number of possible outcomes.
Experiment 1:
 A spinner has 4 equal sectors colored yellow,
blue, green and red. After spinning the spinner,
what is the probability of landing on each color?
Outcomes:
The possible outcomes of this experiment are
yellow, blue, green, and red.

12. Probabilities:
 P(yellow) = # of ways to land on yellow = 1
total # of colors 4
 P(blue) = # of ways to land on blue = 1
total # of colors 4

13.  P(green) = # of ways to land on green = 1
total # of colors 4
 P(red) = # of ways to land on red = 1
total # of colors 4

14. Experiment 2:
 A single 6-sided die is rolled. What is the
probability of each outcome? What is the
probability of rolling an even number? of rolling an
odd number?
Outcomes:
 The possible outcomes of this experiment are 1,
2, 3, 4, 5 and 6.

15.  P(1) = # of ways to roll a 1= 1
total # of sides 6
 P(2) = # of ways to roll a 2 = 1
total # of sides 6
 P(3) = # of ways to roll a 3 = 1
total # of sides 6

16.
 P(4) = # of ways to roll a 4 = 1
total # of sides 6
 P(5) = # of ways to roll a 5 = 1
total # of sides 6
 P(6) = # of ways to roll a 6 = 1
total # of sides 6

17. P(even) = # ways to roll an even number= 3= 1
total # of sides 6 2
P(odd) = # ways to roll an odd number = 3= 1
total # of sides 6 2

18. SEATWORK:
I. Give a sample space for each of the following
experiments:
1. Selecting a person from an elective class (give
two sample spaces)
2. Answering a true – false question
3. Selecting a letter at random from the English
alphabet
4. Tossing a single die
5. Tossing a coin three times
6. Selecting a day of the week

19. II. Consider the experiment of drawing a numbers 1
through 10,
7. Give the sample space
8. The event of drawing an odd number is
the subset ___________
9. The event of drawing an even number is
the subset _________
10. The event of drawing a prime number is
the subset __________

20. 1. A die is thrown once. What is the probability that
the score is a factor of 6?
A. 1/6 C. 2/3
B. ½ D. 1

21. 2. The diagram shows a spinner made up of a piece
of card in the shape of a regular pentagon, with a
toothpick pushed through its center. The five
triangles are numbered from 1 to 5.
The spinner is spun until it lands on one of the
five edges of the pentagon. What is the probability
that the number it lands on is odd?
A. 1/5 C. 1/2
B. 2/5 D. 3/5

22. 3. Each of the letters of the word MISSISSIPPI are
written on separate pieces of paper that are then
folded, put in a hat, and mixed thoroughly.
One piece of paper is chosen (without looking)
from the hat. What is the probability it is an I?
A. 4/11 C. 1/3
B. 2/5 D.1/4

23. 4. There are 10 marbles in a bag: 3 are red, 2 are
blue and 5 are green.
The contents of the bag are shaken before Maxine
randomly chooses one marbles from the bag.
What is the probability that she doesn't pick a red
marbles?
A. 3/10 C. 3/7
B. 2/5 D. 7/10

24. 5. What is the probability that the card is either a
Queen or a King in a deck of cards?
A. 4/13
B. 2/13
C. 1/8
D. 2/11

25. 1. The factors of six are 1, 2, 3 and 6, so the
Number of ways it can happen = 4
There are six possible scores when a die is
thrown, so the Total number of outcomes = 6
So the probability that the score is a factor of six =
4/6 = 2/3

26. 2. There are three odd numbers (1, 3 and 5), so the
Number of ways it can happen = 3
There are five numbers altogether, so the Total
number of outcomes = 5
∴ The probability the number is odd = 3/5

27. 3. There are 4 I's in the word MISSISSIPPI, so the
Number of ways it can happen = 4
There are 11 letters altogether in the word
MISSISSIPPI, so the Total number of outcomes =
11
So the probability the letter chosen is an I=
4/11

28. 4. There are 7 marbles that are not red: 2 blue and
5 green
The Number of ways it can happen = 7
The Total number of outcomes = 10

29. 5. There are 4 Queens and 4 Kings, so the Number
of ways it can happen = 8
There are 52 cards altogether, so the Total
number of outcomes = 52

30.  Probabilities may be assigned by observing a
number of trials and using the frequency of
outcomes to estimate probability.
 For example, the operator of a concession stand
at a park keeps a record of the kinds of drinks
children buy. Her records show the following:

31. Drink Frequency
Cola 150
Lemonade 275
Fruit Juice 75
500

32. In order to estimate the probability that a child will
buy a certain kind of drink, we compute the
relative frequency of each drink.
DRINK FREQUENCY RELATIVE
FREQUENCY
150 = .30
Cola 150 500
Lemonade 275 275 = .55
500
Fruit Juice 75 75 = .15
500
500 1.00

33. 2. A college has an enrolment of 1210 students.
The number in each class is as follows.
CLASS NUMBER OF
STUDENTS
Freshman 420
Sophomore 315
Junior 260
Senior 215

34. 3. The owner of a hamburger stand found that 800
people bought hamburgers as follows:
KIND OF BURGER FREQUENCY
Mini burger 140
Burger 345
Big Burger 315