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All courses Algebra II · 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 \(\text{one}\) 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

List the complete outcome space

\[S=H,T\]

One coin flip has exactly two possible outcomes: heads or tails.

02

Assign fair probabilities

\[P(H)=1/2;~P(T)=1/2\]

A fair coin gives the two outcomes equal probability.

03

Verify the probability total

\[P(H)+P(T)=1/2+1/2=1\]

A valid probability model assigns total probability 1 across all outcomes.

04

Identify the success event

\[\text{Outcomes}~H~\text{and}~T~\text{each}~\text{have}~\text{probability}~1/2,~\text{total}~\text{probability}~1,~\text{and}~H~\text{is}~\text{the}~\text{success}~\text{event}.\]

Because heads is defined as success, the success event contains only outcome H.

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Another way

  1. Use a two-row model: H maps to one half and success; T maps to one half and failure.

!

Common mistake

Do not assign probability 1 to heads merely because heads is called success. Success names the event; fairness still gives it probability one half.

Solution walkthrough video