3.1 Choosing Paths . . . More Area Models
Kenisha is designing a game involving paths through the woods that lead to caves. Before the
game is played the player chooses either Cave A or Cave B. Next, the player starts at the
beginning and chooses a path at random at each fork. If the player lands in the cave that was
chosen in the beginning, he or she wins a prize.
Are you more likely to end up in cave A or in cave B? Why?
1
We are going to do
an experiment to
find the likelihood
of ending in cave A
or in cave B. We will
use spinners to
randomly choose the
path.
Keep track of the results in the table below.
spin 1
2
3
4
5
6
7
11
12
13
14
cave
spin
8
9
10
cave
1. What is the experimental probability of ending in cave A?
2. What is the experimental probability of ending in cave B?
2
Mike has made this diagram
to help us find the
theoretical probability of
ending in cave A or cave B.
3. Explain what mike has
done so far. Does it look
reasonable?
4. Complete Mike's model to find the theoretical probability
of ending in cave A or Cave B.
5. What is the theoretical probability of ending in cave A?
6. What is the theoretical probability of ending in cave B?
7. Compare the theoretical probabilities to the experimental
probabilities found in questions 1 and 2.
3
Kenisha designs a new version of the game. It has a different
arrangement of paths leading to Caves A and B. She makes the area
model below to analyze the probabilities of ending in each cave.
8. Create a path game that fits the model.
9. Find the probability for each outcome:
P(A)
P(B)
4
5
6