Grinstead-Snell-Probability · Problem 4.1.7

Conditional Probability

Mathematics · pairwise-independence

Problem

A coin is tossed twice. Consider the following events.

A

: Heads on the first toss.

B

: Heads on the second toss.

C

: The two tosses come out the same. (a) Show that

A

B

C

are pairwise independent but not independent. (b) Show that

C

is independent of

A

and

B

but not of

A \cap B