Introduction to Probability · Problem 4.1.50

Conditional Probability — Grinstead & Snell

Mathematics — Probability · independence-sample-space-size

Problem

Prove that, if

A_1, A_2, \ldots, A_n

are independent events defined on a sample space

\Omega

and if

0 < P(A_j) < 1

for all

j

, then

\Omega

must have at least

2^n

points.