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All courses Math III · S-IC.2 48 of 55
Use simulation to decide whether data are consistent with a proposed model.

Build a complete simulation probability table

Problem
Build a complete probability model for one fair coin flip with heads defined as success. Include all outcomes, probabilities, their total, and the success event.
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Hint

List every possible outcome category before assigning probabilities.

A valid discrete model lists mutually exclusive exhaustive outcomes with nonnegative probabilities summing to 1.

Solution walkthrough

01

Define one random action

\[\text{one}~\text{fair}~\text{coin}~\text{flip};~\text{success}=\text{heads}\]

The outcome space must correspond to one simulation trial/action.

02

Assign outcome probabilities

\[{\text{heads}:1/2,\text{tails}:1/2}\]

Use fair face/section counts or object composition under the stated assumptions.

03

Check completeness

\[\text{sum}=1\]

Mutually exclusive exhaustive probabilities total 1.

04

Define success and assumptions

\[\text{success}=\text{heads};~\text{fair}~\text{coin};~\text{independent}~\text{flips}~\text{if}~\text{repeated}\]

Success is a subset of outcomes; assumptions justify probabilities.

05

Submit model

\[\text{outcome}~\text{rows}={\text{heads}:1/2,\text{tails}:1/2};~\text{probability}~\text{sum}=1;~\text{success}~\text{event}=\text{heads};~\text{assumptions}=\text{fair}~\text{coin};~\text{independent}~\text{flips}~\text{if}~\text{repeated}\]

Multi-outcome models use repeated rows rather than one ordered pair.

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Another way

  1. Map equally likely elementary outcomes to broader categories and add their probabilities.

!

Common mistake

Do not list only success or assume unequal categories are equally likely.