2.1 Another Option . . . Area Models
In the Red and Blue game, from Investigation 1.4, we made a tree
diagram to help us find theoretical probability. An area model is
another method that we can use to help us analyze such games.
So . . . how do we make this area model?
How do we use this area model?
1
1.
Draw a square.
Suppose the square has an
area of 1 square unit. We use
the square to represent a
probability of 1.
2. The first bucket has three
equally likely possibilities: red,
green, and another green. Divide
the square above into three
horizontal sections with equal
areas and label the sections.
3. The second bucket has
four equally likely possibilities:
red, green, yellow, and blue.
Next, divide the square above
into four vertical sections
with equal areas and label the
sections.
4. Each small section of our square represents one of the out comes
found in our tree diagram. Label each section according to the outcome.
5. The area of each region represents the probability for each outcome.
a.
b.
c.
d.
e.
RR?
RB?
RG?
RY?
GR?
f.
g.
h.
i.
GB?
GG?
GY?
YY?
2
Using the area model find the
probability for each of the
following events.
a.
b.
c.
d.
e.
f.
P(exactly one red)?
P(rg)?
P(one red and one green)?
P(yg)?
P(at least one green)?
P(both greens)?
3
4
5