Question 1175512: In a group of people, some are in favor of a tax increase on rich people to reduce the federal deficitand others are against it. (Assume that there is no other outcome such as “no opinion” and “do not know.”)Three persons are selected at random from this group and their opinions in favor or against raising suchtaxes are noted. How many total outcomes are possible? Write these outcomes in a sample space S. Drawa tree diagram for this experiment.
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! 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
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