Introduction to Probability · Problem 4.1.8

Conditional Probability — Grinstead & Snell

Mathematics — Probability · mutual-independence

Problem

Let

\Omega = \{a, b, c, d, e, f\}

. Assume that

m(a) = m(b) = 1/8

and

m(c) = m(d) = m(e) = m(f) = 3/16

. Let

A

B

, and

C

be the events

A = \{d, e, a\}

B = \{c, e, a\}

C = \{c, d, a\}

. Show that

P(A \cap B \cap C) = P(A)P(B)P(C)

but no two of these events are independent.