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Probability Basics
Section 6.2.1
Starter 6.2.1
• Roll two dice and record the sum shown.
• Repeat until you have done 20 rolls.
• Write a list of all the possible outcomes
(sums) and how many of each you got.
• Report those totals to me when I call for
them.
– I will record class totals and show the
distribution of outcomes.
Objectives
• Write the sample space for a set of events.
• Count the outcomes in a sample space by
using the multiplication principle.
• Describe what is meant by the
complement of an event.
• Describe what it means to say that two
events are disjoint.
– Use the addition rule for disjoint events to
answer “or” probability questions.
The Sample Space
• The sample space of an event is a listing
of all possible outcomes.
• List all the sums possible in the starter.
S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
• Suppose the question had asked you to do
20 rolls of two dice and note the individual
dice face-up spots as ordered pairs
– Example: (red 3, green 6)
• Write the sample space for rolling two dice
– In other words, write an organized list or table
showing all the possible ordered pairs
The Sample Space of Two Dice
1,1
2,1
3,1
4,1
5,1
6,1
1,2
2,2
3,2
4,2
5,2
6,2
1,3
2,3
3,3
4,3
5,3
6,3
1,4
2,4
3,4
4,4
5,4
6,4
1,5
2,5
3,5
4,5
5,5
6,5
1,6
2,6
3,6
4,6
5,6
6,6
• Notice that each of the 36 outcomes is equally likely
• The sums are not equally likely because each sum has
different numbers of outcomes above
• Compare theoretical probability of each sum with the
empirical probabilities we found in the starter
The Multiplication Principle
• If task A can be done in x ways, and task B
can be done in y ways, then the number of
x y
ways to do both A and B is
– There were 6 ways to roll the red die and 6
ways to roll the white die, so there are 36
ways to roll both dice.
– In yesterday’s starter, there were 2 ways to
toss the first coin and 2 ways to toss the
second coin and 2 ways to toss the third coin,
so there are 8 ways to toss the three coins.
The Rules of Probability
• Rule 1: For any event A:
0  P( A)  1
• Rule 2: If S is the sample space: P(S) = 1
• Rule 3: The complement of event A is the event
that A does not occur
– The Complementary Probability Rule is:
P(Ac) = 1 – P(A)
• Rule 4: Two events A and B are disjoint if they
are mutually exclusive (if A happens, B cannot
and vice-versa).
– The probability of two disjoint events is:
P(A or B) = P(A) + P(B)
• This is called the “disjoint or” rule
Disjoint Examples
• Roll two dice. I will pay you $1 if you get a sum
of 7 or 8.
–
–
–
–
What is event A?
What is event B?
Are A and B disjoint?
What is P(A or B)?
• Choose a student from this class at random. I
will pay you $1 if the student is a senior or a boy.
– What is event A?
– What is event B?
– Are A and B disjoint?
Objectives
• Write the sample space for a set of events.
• Count the outcomes in a sample space by
using the multiplication principle.
• Describe what is meant by the
complement of an event.
• Describe what it means to say that two
events are disjoint.
– Use the addition rule for disjoint events to
answer “or” probability questions.
Homework
• Read pages 318 – 329
• Do problems 9, 12, 15, 18, 20-23