Problem preview

S-MD.7 Warmup M3-055-A07-V03

Analyze decisions and strategies using probability concepts in more complex settings.

Compare insurance expected cost separately from risk protection

Problem

Phone protection costs $\$12~\text{per}~\text{month}$ for $24~\text{months}$; the expected replacement cost without it is $\$180$. Compute total plan cost, compare expected costs, and retain terms and risk-preference caveats.

Answer choices

Choose your path.

Preview only

Treat no-plan expected cost as $288 versus plan cost $288; call them equal while ignoring the stated $180 estimate.

Use costs $288 and $180, favor no plan, but claim expected cost makes protection terms and risk preference irrelevant.

The plan costs $288 versus $180 expected unprotected cost, so expectation favors no plan; protection terms and risk preference may still matter.

Treat the plan as $12 total versus $180 unprotected; favor the plan on expectation and risk without multiplying 24 months.

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Curriculum context

Course: Math III
Standard: S-MD.7
Category: Statistics and Probability
Domain: Using Probability to Make Decisions
Objective: Analyze decisions and strategies using probability concepts in more complex settings.
Problem type: Compare insurance expected cost separately from risk protection