Contingency Tables and Probability

Contingency Tables

• Used to lay out information for calculating probabilities.
• Probabilities are calculated using row and column totals.

Examples

• Probability of a random employee being a Democrat: P(Democrat) = \frac{Total \, Democrats}{Total \, Employees}
  • From the example: P(Democrat) = \frac{68}{140}
• Probability of a random employee being an executive: P(Executive) = \frac{Total \, Executives}{Total \, Employees}
  • From the example: P(Executive) = \frac{48}{140}
• Probability of a random employee being both a Democrat and an executive: P(Democrat \, and \, Executive) = \frac{Number \, of \, Democrat \, Executives}{Total \, Employees}
  • From the example: P(Democrat \, and \, Executive) = \frac{5}{140}
• Conditional Probability: Probability of being a Democrat given the employee is an executive: P(Democrat | Executive) = \frac{Number \, of \, Democrat \, Executives}{Total \, Executives}
  • From the example: P(Democrat | Executive) = \frac{5}{48}
  • With conditional probability, focus only on the given row or column.