1. Describe two real-life events that are dependent.
2. Use the information on
page 723
to explain how probability applies to basketball. Explain how a value such as one of those in the table could be used to find the chances of Yao Ming making 0, 1, or 2 of 2 successive field goals, assuming the 2 field goals are independent, and a possible reason why 2 field goals might not be independent.
12-4
Multiplying Probabilities
Main Ideas
. Find the probability
of independent
events
find the probability
of dependent
events
New Vocabulary
andingan
GET READY for the Lesson
Yao Ming, of the Houston Rockets, has one
of the best field-goal percentages in the
National Basketball Association. The table
shows the field-goal percentages for three
Season TG4
years of his career. For any year, you can
2002-6588
determine the probability that Yao will
2005-04 22
make two field goals in a row based on 2004-05 52
the probability of his making one field goal. Source: nba.com
Probability of Independent Events in a situation with two events like
shooting a field goal and then shooting another, you can find the
probability of both events occurring if you know the probability of each
event occurring. You can use an area diagram to model the probability of
the two events occurring
Algebra Lab
Area Diagrams
Suppose there are 1 red and
Colored
3 blue paper clips in one
drawer and 1 gold and 2 silver
paper clips in another drawer.
The area diagram represents
the probabilities of choosing
one colored paper clip and one
A
metallic paper clip if one of
each is chosen at random. Metallic
For example, rectangle A
represents drawing 1 silver
clip and 1 blue dip
С
D
MODEL AND ANALYZE
1. Find the areas of rectangles A, B, C and D. Explain what each represents.
2. Find the probability of choosing a red paper clip and a silver paper clip.
3. What are the length and width of the whole square? What is the area?
Why does the area need to have this value?
4. Make an area diagram that represents
the probability of each outcome if you
spin each spinner once label the
diagram and describe what the area of
each rectangle represents.
In Exercise 4 of the lab, spinning one spinner has no effect on the second
spinner. These events are independent.
Lesson 12-4 Multiplying Probabilities 703
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