Transcript Probability - Cloudfront.net

Counting Methods
Lesson 11-5
Pg. # 426-428
CA Content Standards
Statistics, Data Analysis, and Probability 3.1 ***:
I represent all possible outcomes of compound
events in an organized way and express the
theoretical probability of each outcome.
Statistics, Data Analysis, and Probability 3.3***:
I represent probabilities as ratios and percentages
between 0 and 100.
Vocabulary: TREE DIAGRAM
A diagram used to organize outcomes of an
experiment to make them easier to count.
Vocabulary:
COUNTING PRINCIPLE
If one choice can be made in m ways and
a second choice can be made in n ways,
then the two choices can be made together
in m x n ways.
Objective
Use a tree diagram or the counting principle to
find the total number of outcomes for an event.
Math Link: You can use what you know about
making tables and tree diagrams to find all
possible outcomes.
Example 1.
The cooking club is having a sandwich
fundraiser. A sandwich consists of one choice
of bread and one choice of filling. How many
different kinds of sandwiches can be made
with the following ingredients?
Bread: Pita, Tortilla
Filling: Chicken, Beef, Vegetable
You can use a tree diagram…
To represent the different kinds of sandwiches.
Sandwich Fundraiser
Sandwich
Pita
Chicken
Outcome 1
Beef
Outcome 2
Tortilla
Vegetable
Outcome 3
Chicken
Outcome 4
Beef
Outcome 5
Menu includes: pc, pb, pv, tc, tb, tv
Vegetable
Outcome 6
Example 2.
One of each type of sandwich is prepared. You choose
one without looking. Find the probability of getting a beef
sandwich.
The menu includes 6 kinds of sandwiches: pc, pb, pv, tc,
tb, tv
2 kinds of sandwiches have beef: pb, tb
So…
P(beef) = 2/6 = 1/3 = 33%
The probability of getting a beef sandwich is about 33%.
Example 3.
If there are three kinds of breads and four kinds of fillings
at the fundraiser, how many different kinds of
sandwiches can be made?
Use the counting principle.
If there are m possible outcomes for the first event and n possible
outcomes for the second event, then there are m x n possible
outcomes.
Possible
Breads
Sandwiches
3
x
Possible
Fillings
Kinds of
4=
12
Twelve different kinds of sandwiches could be made.
Moral of the Story
Use tree diagrams to organize possible
outcomes. Also, if there are m possible
outcomes for the first event and n
possible outcomes for the second
event, then there are m x n total
possible outcomes.