Download Lesson 5.2.6 Day 1 – Teacher Notes Standard

Lesson 5.2.6 Day 1 – Teacher Notes
Standard:
7.SP.C.8a and b Find probabilities of compound events using organized lists, tables, tree
diagrams, and simulation.
a) Understand that, just as with simple events, the probability of a compound event is the
fraction of outcomes in the sample space for which the compound event occurs.
b) Represent sample spaces for compound events using methods such as organized lists,
tables and tree diagrams. For an event described in everyday language (e.g., "rolling
double sixes"), identify the outcomes in the sample space which compose the event.
• Full mastery of the standard can be expected by the end of the chapter.
Lesson Focus:
The focus of today is finding probability using tables, (rectangular models). (5-78)
• I can choose the appropriate method such as organized lists, tables, and tree
diagrams to represent sample spaces for compound events.
Calculator: Yes
Literacy/Teaching Strategy: Reciprocal Teaching (Intro); Hot Potato (5-78)
Bell Work
Day 1
In Lesson 5.2.5, you used systematic lists,
probability tables, and probability trees to organize
the outcomes of different probability
situations. Today you will use a probability table to
help organize events when one outcome is more
likely than another.
5-76. Nina is buying a new pet fish. At the pet store, the fish
tank has an equal number of two kinds of fish: tetras and
guppies. Each kind of fish comes in four different colors:
yellow, orange, blue, and silver. There are an equal number of
each color of fish in the tank.
a. If Nina scoops out a fish at random, what is the probability
that she will scoop out a silver tetra? Show how you decided.
5-76 cont.
b. Nina set up the table below, to organize the different possible
outcomes. She represented the kind of fish on one side of her table
and the color possibilities on the other. What do the fractions inside
her table represent?
c. As Nina looked at her work, she noticed that her table looked a
lot like a rectangle with the area divided into parts. “Could that help
me calculate the probabilities?” she wondered. She used the length
and width of the silver tetra section to set up this equation: 1  1 = 1 .
4
2
8
How does this equation relate to the length, width, and area of this
section of the rectangle? Does this match the probability you found
in part (a)?
d. What is the area of the complete large rectangle?
5-77. TESTING THE AREA MODEL
Nina decided to see if thinking about finding area would help
find other probabilities. She put three cubes in a bag: two blue
cubes and one yellow cube. She pulled one cube out, put it
back in the bag, and then drew another.
a. Use a systematic list or a probability tree to organize the
possible color combinations she could draw. How many are
there? What is P(blue and blue)?
b. This time, Nina made the table at right. Based on the table,
what is the probability of drawing two blue blocks? Is this the
same probability you found in part (a)?
5-77 cont.
c. Looking at her work, Edwin said, “I think I can simplify
this diagram.” His rectangle is shown at right. What is
the area of the section representing blue and blue? Does
this match the probability that Nina found?
5-78. The pet store sells a lot of pet food. On a slow
day at the pet store, three people buy cat food, two
people buy dog food, and one person buys food for a
pet snake. If half of the customers pay with cash and
half pay with credit card, what is the probability that a
customer buying pet food will buy dog food with cash?
Set up an area model like Edwin’s in part (c) of problem
5-77 to help you find the probability.
Practice
Find the area of these rectangles:
a. b.
d.
b.
c.
e.