📊

Creating a Contingency Table for Delivery

May 9, 2025

Building a Contingency Table for On-time Delivery

Introduction

  • Objective: Build a contingency table using probabilities of document delivery by two services.
  • Example problem: Two copies of a document sent using Service A and Service B.

Given Probabilities

  • Probability of on-time delivery with:
    • Service A: 0.9
    • Service B: 0.8
    • Both Services A and B: 0.75

Table Setup

  • Rows: Events associated with Service A
    • Event A: Document arrives on time
    • Not A: Document does not arrive on time
    • Total probability of A: 0.9
  • Columns: Events associated with Service B
    • Event B: Document arrives on time
    • Not B: Document does not arrive on time
    • Total probability of B: 0.8

Calculating Probabilities

  1. Intersection of A and B:

    • Probability (A and B) = 0.75
  2. Row A:

    • Total Probability = 0.9
    • Calculate missing cell: 0.9 - 0.75 = 0.15
  3. Column B:

    • Total Probability = 0.8
    • Calculate missing cell: 0.8 - 0.75 = 0.05
  4. Total Table Probability:

    • Must sum to 1.0
    • Accounted 0.8 for B, remaining: 1.0 - 0.8 = 0.2
  5. Row Not A:

    • Total Probability = 0.1 (calculated: 1.0 - 0.9)
    • Fill remaining cells using arithmetic.

Verification

  • Row Totals:
    • A: 0.75 + 0.15 = 0.9
    • Not A: 0.05 + 0.05 = 0.1
  • Column Totals:
    • B: 0.75 + 0.05 = 0.8
    • Not B: 0.15 + 0.05 = 0.2
  • Overall Check:
    • Sum of probabilities: 0.8 + 0.2 = 1.0
    • 0.9 + 0.1 = 1.0

Conclusion

  • The contingency table accurately reflects the given probabilities and checks out through arithmetic and logical verifications.