Measure, Integration & Real Analysis · Problem 12.5

Probability Measures — Sheldon Axler

Mathematics — Measure Theory · pairwise-independence-not-joint

Problem

Give an example of a probability space

(\Omega, \mathcal{F}, P)

and events

A, B_1, B_2

such that

A

and

B_1

are independent,

A

and

B_2

are independent, but

A

and

B_1 \cup B_2

are not independent.