Suppose A and B are independent events of a sample space S P

Suppose A and B are independent events of a sample space S. Prove that A\' and B\' are independent events.

Strategy of Prood: in order to show that A\' and B\' are indepdent, we need to show that P(A\')*P(B\') = ______________.

Proof: Suppose A and B are indepednet events of a sample space S/

P(A\')*P(B\') = [1- __________ ] [1 - _______ ] by Theorem_______. = 1 - P(A) - P(B) + P(A)*P(B) = 1 - [P(A) + P(B) ___________________ ] = 1 - [P(A) + P(B) - P(A n B) since _____________________________. = 1 - P( _________________________) by Theorem _____________________. = P[( ________________)\' ] by Theorem ____________________. = P(A\' n B\') by ____________________________________.

Therefore, __________________________________________________________.

Solution