Compound Probability and Overlapping Inequities Vocabulary Review

How to Use

• Review each term and example before your quiz.
• Connect math definitions to real situations about stacked barriers and fairness.
• Keep this sheet in your Equity in Numbers Student Journal.
• Remember: Probability helps us see how different barriers connect — and how equity solutions can connect too.

Compound Probability

• Definition: The probability of two or more events happening together or in combination.
• Math Example: P(L and H) = 0.26 → 26%.
• Real-Life Example: A resident experiences both low income and limited health access.
• Fairness Example: Shows how barriers can stack on top of each other, increasing inequity.

Intersection (∩)

• Definition: The probability that two events happen at the same time.
• Math Example: P(L ∩ H) = 0.26.
• Real-Life Example: People who have both low income and limited healthcare access.
• Fairness Example: The intersection shows where needs overlap and support must be targeted.

Union (∪)

• Definition: The probability that at least one of two events occurs.
• Formula: P(A ∪ B) = P(A) + P(B) – P(A ∩ B).
• Math Example: P(L ∪ H) = 0.45 + 0.38 – 0.26 = 0.57 (57%).
• Real-Life Example: People who have either low income or limited health access (or both).
• Fairness Example: The union shows how many people need at least one kind of support.

Complement (Aᶜ)

• Definition: The event that the original event does not happen.
• Formula: P(Aᶜ) = 1 – P(A).
• Math Example: If P(L ∪ H) = 0.57, then P(neither) = 0.43.
• Real-Life Example: Residents who do not face either barrier.
• Fairness Example: Shows who already has resources — useful for comparing conditions.

Conditional Probability

• Definition: The probability of one event occurring given that another has already occurred.
• Formula: P(A | B) = P(A ∩ B) ÷ P(B).
• Math Example: P(H | L) = 0.26 ÷ 0.45 = 0.58 (58%).
• Real-Life Example: 58% of low-income residents also have limited healthcare access.
• Fairness Example: Shows how one inequity increases the likelihood of another.

Independence

• Definition: Two events are independent if the probability of one does not change when the other happens.
• Math Check: Compare P(A | B) to P(A). If they’re equal, events are independent.
• Math Example: P(H) = 0.38 vs P(H | L) = 0.58 → Not independent.
• Real-Life Example: Low income does affect access to healthcare.
• Fairness Example: Non-independence shows structural connections between barriers.

Dependent Events

• Definition: Events where one outcome affects the other.
• Math Example: P(H | L) ≠ P(H).
• Real-Life Example: If having low income increases the chance of limited healthcare, the events are dependent.
• Fairness Example: Dependence shows how systemic issues link across areas like income and transportation.

At Least One

• Definition: The probability that one or more events happen.
• Formula: P(At Least One) = 1 – P(None).
• Math Example: If P(neither) = 0.43, then P(At Least One) = 0.57.
• Real-Life Example: 57% of residents face one or more barriers.
• Fairness Example: Quantifies the proportion of the community needing some type of support.

Exactly Two Events

• Definition: When a person experiences two out of three possible events.
• Math Example: P(Exactly 2 Barriers) = Sum of each two-way intersection – 2×(three-way overlap).
• Real-Life Example: Residents who struggle with income and transportation, but have health access.
• Fairness Example: Helps target interventions for people facing multiple barriers simultaneously.

Overlapping Inequities

• Definition: When two or more social barriers affect the same individuals or communities.
• Math Example: P(L ∩ H) = 26% overlap between income and health barriers.
• Real-Life Example: Families who both lack transportation and health coverage.
• Fairness Example: Overlaps reveal how systems of inequality interact — and where change is most needed.

Interpretation

• Definition: Explaining what probability results mean in real contexts.
• Math Example: “57% of residents face at least one barrier — nearly 3 in 5 people.”
• Real-Life Example: Data helps policy leaders prioritize resources for high-barrier communities.
• Fairness Example: Interpretation transforms numbers into stories of advocacy and solutions.

Summary of Math + Fairness Connections

Concept	Math Focus	Fairness Connection
Intersection (∩)	Both events occur	Shows stacked barriers
Union (∪)	At least one event	Reveals who needs any support
Complement (Aᶜ)	Neither event occurs	Identifies those without barriers
Conditional Probability	Given that one happened	Measures linked inequities
Independence	Compare P(A	B) vs P(A)
Overlapping Inequities	Multiple events at once	Defines where change is most urgent