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Sample points are the possible outcomes that can occur in a probability experiment. In the context of the zoning change process in Milford, each combination of decisions from the planning commission and the city council forms a unique sample point. Think of sample points as the "final results" you might see at the end of the entire process.
To understand this concept, remember that each decision-making step yields different scenario outcomes. For the zoning change, the planning commission can either make a positive recommendation (P) or a negative one (N). Following this, the city council can either approve (A) or disapprove (D) the recommendation they receive. These decision points combine to create distinct sample points.

• Planning Commission Positive, City Council Approves (PA)
• Planning Commission Positive, City Council Disapproves (PD)
• Planning Commission Negative, City Council Approves (NA)
• Planning Commission Negative, City Council Disapproves (ND)

In total, there are 4 sample points in this experiment: PA, PD, NA, and ND. Visualizing these options can help in grasping the entire range of possible outcomes.

A tree diagram is a great tool to visualize the sequence of events in a probability experiment by laying out the possible outcomes in a branching format. It helps represent each step in the process and shows how outcomes depend on each previous decision.
For the zoning change process, start by visualizing the first step, which is the planning commission's review. From a starting node, draw two branches corresponding to their possible decisions: a positive recommendation (P) and a negative one (N).
Then, for each of these branches, add another set of branches to account for the city council's decision. If the commission recommends positively (P), create branches for the council's approval (A) and disapproval (D). Similarly, if the commission recommends negatively (N), create branches for approval (A) and disapproval (D).
This branching approach creates a diagram with 4 end points:

• PA: Planning Positive, Council Approves
• PD: Planning Positive, Council Disapproves
• NA: Planning Negative, Council Approves
• ND: Planning Negative, Council Disapproves

Each path from start to finish represents one sample point from our previous explanation. The clarity of a tree diagram comes from its ability to show all outcomes at a glance.

The zoning change process in Milford is an example of a decision-making procedure involving two sequential reviews. Each step involves a probability experiment because it has two possible outcomes, much like flipping a coin.
Initially, the planning commission reviews a zoning change application. Their decision is straightforward: they either give a positive recommendation (P) or a negative one (N). This step establishes the trajectory for the subsequent city council review.
During the city council review, their decision depends in part on what recommendation they receive. They can approve (A) the recommendation they agree with or disapprove (D) if they do not. Despite the council having the final say, the initial recommendation greatly influences the process.
Understanding this zoning change process illuminates how decisions in a bureaucratic setup unfold. The process shows how sequential decisions can shape the final outcome, demonstrating the complexity of probabilities even in relatively simple systems. This knowledge is vital for developers and other stakeholders involved in similar decision pathways.