Introduction to Probability · Problem 4.1.51

Conditional Probability — Grinstead & Snell

Mathematics — Probability · conditional-probability-inequality

Problem

Prove that if

P(A|C) \ge P(B|C) \quad \text{and} \quad P(A|\tilde{C}) \ge P(B|\tilde{C}) ,

then

P(A) \ge P(B)