Question 1175512
Let's break down this probability problem.

1. Total Possible Outcomes

Each person can have two possible opinions: "in favor" (F) or "against" (A).
We're selecting three people, so we have 2 options for each person.
The total number of outcomes is 2 * 2 * 2 = 2^3 = 8.
2. Sample Space (S)

We can list the possible outcomes as ordered triples, where each position represents the opinion of one of the three people:

S = {
(F, F, F),
(F, F, A),
(F, A, F),
(F, A, A),
(A, F, F),
(A, F, A),
(A, A, F),
(A, A, A)
}
3. Tree Diagram

Here's how to draw the tree diagram:

First Person:

Start with a single point.
Branch out to two possibilities: F (in favor) and A (against).
Second Person:

From each of the first person's branches (F and A), branch out again to two possibilities: F and A.
This results in four branches.
Third Person:

From each of the second person's branches, branch out again to two possibilities: F and A.
This results in eight final branches, each representing one of the outcomes in the sample space.
Here's a text representation of the tree diagram:

                  Start
                 /     \
                F       A
               / \     / \
              F   A   F   A
             / \ / \ / \ / \
            F A F A F A F A
Outcomes:
Following the branches from left to right, we get the outcomes:
FFF
FFA
FAF
FAA
AFF
AFA
AAF
AAA