Show directly that Proposition 2.1 holds for the conditional probability PF . In particular, for any events E and F E (E c | F) = 1 E (E | F).

Proposition 2.1 : P(E c ) = 1 P(E) for any E F

Hint: Write the sample space S=E union E^c and use the fact that P(E^c)=1-P(E) and the definition of P(E | F). Remember your properties of unions and intersections of sets.