Transcript 13-1 Representing Sample Spaces

13-1 Representing Sample
Spaces
You calculated experimental probability.
• Use lists, tables, and tree diagrams to
represent sample spaces.
• Use the Fundamental Counting Principle to
count outcomes.
Experiments, Outcomes, and Events
The sample space of an experiment is the set of all
possible outcomes.
Tree diagram is an organized table of line segments
(branches) which shows possible experiment outcomes.
One red token and one black token are placed in a bag. A token is
drawn and the color is recorded. It is then returned to the bag and a
second draw is made. Represent the sample space for this
experiment by making an organized list, a table, and a tree diagram.
Organized List Pair each possible outcome from the first drawing
with the possible outcomes from the second drawing.
R, R
R, B
B, B
B, R
Table List the outcomes of the first
drawing in the left column and those
of the second drawing in the top row.
Tree Diagram
One yellow token and one blue token are placed in a bag. A
token is drawn and the color is recorded. It is then returned
to the bag and a second draw is made. Choose the correct
display of this sample space.
A.
B.
C.
D. Y, Y; B, B; Y, B
Experiment Stages
Two-stage experiment – an experiment with two
stages or events (like the 1st problem).
Multi-stage experiment – experiments with more
than two stages.
Multi-Stage Tree Diagrams
CHEF’S SALAD A chef’s salad at a local restaurant comes
with a choice of French, ranch, or blue cheese dressings
and optional toppings of cheese, turkey, and eggs. Draw a
tree diagram to represent the sample space for salad
orders.
Answer:
The sample space is the
result of 4 stages.
● Dressing (F, R, or BC)
● Cheese (C or NC)
● Turkey (T or NT)
● Eggs (E or NE)
Draw a tree diagram with
4 stages.
BASEBALL GAME In the bleachers at a major league game
you can purchase a hotdog, bratwurst, or tofu dog. This
comes with the optional choices of ketchup, mustard,
onions, and/or relish. How many stages are in the sample
space?
A. 3
B. 4
C. 5
D. 6
The Fundamental Counting Principle
• If you have 2 events: 1 event can occur m ways and
another event can occur n ways, then the number of
ways that both can occur is m*n
• Event 1 = 4 types of meats
• Event 2 = 3 types of bread
• How many different types of sandwiches can you
make?
• 4*3 = 12
p. 917
3 or more events:
• 3 events can occur m, n, & p ways, then the
number of ways all three can occur is m*n*p
• 4 meats
• 3 cheeses
• 3 breads
• How many different sandwiches can you
make?
• 4*3*3 = 36 sandwiches
• At a restaurant at Cedar Point, you have the
choice of 8 different entrees, 2 different
salads, 12 different drinks, & 6 different
deserts.
• How many different dinners (one choice of
each) can you choose?
• 8*2*12*6=
• 1152 different dinners
Use the Fundamental Counting Principle
CARS New cars are available with a wide
selection of options for the consumer.
One option is chosen from each category
shown. How many different cars could a
consumer create in the chosen make
and model?
Use the Fundamental Counting Principle.
exterior interior
color
color
seat
engine
computer wheels doors
possible
outcomes
11 × 7 × 5 × 3 × 6 × 4 × 3 = 83,160
Answer: So, a consumer can create 83,160 different
possible cars.
BICYCLES New bicycles are available
with a wide selection of options for
the rider. One option is chosen from
each category shown. How many
different bicycles could a consumer
create in the chosen model?
A. 3,888
B. 3,912
C. 4,098
D. 4,124
13-1 Assignment
p. 918, 6-8, 15-18, 20