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Notes Over 12 - 4
Counting Outcomes and Theoretical Probability
1. A school team sells caps in two colors (blue or white), two
sizes (child or adult), and two fabrics (cotton or polyester).
Draw a tree diagram to find the number of cap choices.
child
blue
adult
child
white
adult
cotton
polyester
cotton
polyester
cotton
polyester
cotton
polyester
There are 8
possible cap
choices.
Notes Over 12 - 4
Counting Outcomes and Theoretical Probability
Counting Principle
If there are m ways of making one choice, and
n ways of making a second choice, then there
are m  n ways of making the first choice
followed by the second choice.
Notes Over 12 - 4
Counting Outcomes and Theoretical Probability
Theoretical Probability
number of favorable outcomes
Pevent  
number of possible outcomes
Notes Over 12 - 4
Counting Outcomes and Theoretical Probability
2. A freshman class sells cold drinks. Customers
can choose small, medium, or large. There are five
drinks: cola, diet cola, root beer, lemonade, and
water. Customers can choose ice or no ice. Use the
counting principle to find the total number of
possibilities.
3  5  2  30
What is the theoretical
probability that a customer
will order a medium diet coke
with no ice?
1
30
Notes Over 12 - 4
Counting Outcomes and Theoretical Probability
3. Draw a tree diagram to find the sample space for tossing
two coins. Then find the probability of tossing two heads.
heads
heads
tails
heads
tails
tails
There are 4 possible
outcomes.
Only one outcome is
tossing two heads.
1
Ptossing two heads  
4
Notes Over 12 - 4
Counting Outcomes and Theoretical Probability
4. In some state lotteries, the winning number is made up
of four digits chosen at random. Suppose a player buys two
tickets with different numbers. What is the probability
that the player has a winning ticket?
(each digit can be a number from 0 to 9)
10  10  10  10 10,000
2
1
Pwinning ticket  

10,000
5,000
Pg. 629 #1 – 3, 4 – 17
Counting Outcomes and Theoretical Probability
1. There are 3 ways of performing Task A. There are 4 ways
of performing Task B. Use a tree diagram to find the number
of ways there are to perform Task A and then Task B.
1
2
3
1
2
3
4
1
2
3
4
1
2
3
4
There are
12 possible
ways.
Pg. 629 #1 – 3, 4 – 17
Counting Outcomes and Theoretical Probability
2. There are 8 roads leading from Marsh to Taft and 7 roads
leading from Taft to Polk. How many possible routes are
there for driving from Marsh to through Polk?
8 7  56
There are
56 possible
ways.
Pg. 629 #1 – 3, 4 – 17
Counting Outcomes and Theoretical Probability
3. Find the probability of rolling a 3 on each of two
number cubes.
6  6  36
There are 36 possible ways.
There is only one way of
rolling a 3 on both of them.
1
Prolling a 3 on both  
36
Pg. 629 #1 – 3, 4 – 17
Counting Outcomes and Theoretical Probability