Pre-Algebra
Notes 12.4
Counting Outcomes and Theoretical Probability
Objectives: SWBAT
1.
2.
Counting Possible Choices
1. A school team sells caps in two colors – blue or black, two sizes – child or adult, and
two fabrics – cotton or polyester. Draw a TREE DIAGRAM to find the number of cap
choices.
2. Suppose the caps also come in white. Draw a TREE DIAGRAM. How many choices
are there?
Another way to solve these problems is to use the _________________ ________________.
3. Suppose there are 30 students in this class and each person has exactly five books.
What is the total number of books?
This is an example of the __________________ ___________________.
1
DEFINITION: COUNTING PRINCIPLE
If one thing can happen in _____ ways and another thing can happen in _____ ways, then
the two things together can happen in _____ ways! (Just multiply the numbers together!)
The Counting Principle is particularly useful when a tree diagram would be too large to
draw!!!!!
4. You are buying stationary. How many two-letter
monograms are possible for your new stationary?
5. How many three-letter monograms are possible?
6. How many five-letter license plates can be made if the letters O and I cannot be used?
THEORETICAL PROBABILITY
7. Use a tree diagram to find the sample space for tossing two coins. Then find the
probability of tossing two tails.
2
8. You toss two coins. Find P(one head and one tail).
9. Many people play lottery games without knowing the probability of winning. 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?
10. A lottery uses five digits chosen at random. Find the probability of buying a winning
ticket.
3
Pre-Algebra Objectives 12.4
The student should be able….
1. To use a tree diagram and the Counting Principle
to count possible choices.
2. To find theoretical probability by counting
outcomes.
4