Question

Probability:

If events A, B, and C are independent.
Prove (A or B) and C is independent.

Answer 1

\[P( (A \cup B)C )= P( (AC) \cup (BC) ) = P(AC) + P(BC) - P( ABC ) \]
\[= P(A)P(C) + P(B)P(C) - P(A)P(B)P(C) \]
\[= P(C)(P(A) + P(B) - P(A)P(B)) = P(C)P(A \cup B)\]

Answer 2

easy