CHAPTER 4.1
Sample
Spaces and
Probability
PROBABILIT Y
 “Life is a school of probability” ~ Walter Bagehot
 “The only two sure things are death and taxes” ~ cynical
philosopher
 “Statistically, the probability of any one of us being here
is so small that you'd think the mere fact of existing
would keep us all in a contented dazzlement of surprise”
~ Lewis Thomas
PROBABILIT Y
 Probability can be defined as the chance of an event
occurring
 A probability experiment is a chance process that
leads to well-defined results called outcomes
 An outcome is the result of a single trial of a
probability experiment
 A sample space is the set of all possible outcomes of
a probability experiment
EXAMPLES OF SAMPLE SPACE AND
PROBABILIT Y EXPERIMENTS
Experiment
Toss one coin
Roll a die
Answer a true/false question
Toss two coins
Sample Space
SAMPLE SPACE
 Find the sample space for rolling two dice
SAMPLE SPACE
 Find the sample space for the gender of the children
if a family has three children. Use B for boy and G for
girl.
TREE DIAGRAM
 A tree diagram is a device consisting of line
segments emanating from a starting point and also
from the outcome point. It is used to determine all
possible outcomes of a probability experiment
MAKE A TREE DIAGRAM THE FAMILY
WITH 3 CHILDREN
EVENT
 An event consists of a set of outcomes of a
probability experiment
 An event with one outcome is called a simple event
 A compound event consists of two or more outcomes
or simple events
THE THREE T YPES OF PROBABILIT Y
1. Classical or theoretical
2. Empirical or Relative frequency or Experimental
3. Subjective
CLASSICAL PROBABILIT Y
 Classical probability uses sample spaces to determine the
numerical probability that an event will happen. You do not
actually perform the experiment to determine the probability.
 Classical probability assumes that all outcomes in the sample
space are equally likely to occur.
FORMULA FOR CLASSICAL PROBABILIT Y
 The probability of any event E is the number of outcomes in E
divided by the total number of outcomes in the sample space.
 Denoted by
n( E )
P( E ) 
n( S )
RANGE OF VALUES FOR PROBABILIT Y
 What is the probability that the sun will rise tomorrow?
 What is the probability that Indiana Jones will come crashing
through our window?
 What is the probability of getting heads when a coin is
flipped?
ROUNDING RULES
 Probabilities should be expressed as reduced fractions or
rounded to two or three decimal places.
 When the probability of an event is an extremely small
decimal, round to the first nonzero digit after the decimal
point.
 For example: 0.0000587 would be rounded to 0.00006
EQUALLY LIKELY EVENTS
 Equally likely events are events that have the same
probability of occurring.
 For example, flipping a coin and getting heads or tails
FIND THE PROBABILIT Y OF EACH EVENT
USING A SINGLE DIE
1. P(3)
2. P(even)
3. P(odd)
4. P(prime)
5. P(4 or 5)
6. P(value less than 7)
FIND THE PROBABILIT Y FOR EACH EVENT
USING A STANDARD DECK OF CARDS
1. P(jack)
2. P(heart)
3. P(black ten)
4. P(six of clubs)
5. P(3 or 6)
6. P(3 or diamond)
GENDER OF CHILDREN
 If a family had three children, find the probability that exactly
two of the three children are girls.
 Find the probability that at least one of the three children is a
boy.